Séminaires : Séminaire d'Algèbre

Equipe(s) Responsable(s)SalleAdresse
Groupes, Représentations et Géometrie
J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Info sur https://researchseminars.org/seminar/paris-algebra-seminar

Le séminaire est prévu en présence à l'IHP et à distance. Pour les liens et mots de passe, merci de contacter l'un des organisateurs ou de souscrire à la liste de diffusion https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. L'information nécessaire sera envoyée par courrier électronique peu avant chaque exposé. Les notes et transparents sont disponibles ici.


Since March 23, 2020, the seminar has been taking place remotely. For the links and passwords, please contact one of the organizers or

subscribe to the mailing list at https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. The connexion information will be emailed shortly before each talk. Slides and notes are available here.


Séances à suivre

Orateur(s)Titre Date DébutSalleAdresseDiffusion
+ Baptiste ROGNERUD The fractionally Calabi-Yau combinatorics of the Tamari lattice 03/06/2024 14:00 IHP et Zoom

A poset is said to be fractionally Calabi-Yau if the bounded derived category of its incidence algebra over a field is fractionally Calabi-Yau. In other words, a power of the Serre functor is isomorphic to a shift. When going from a poset to its derived category, one looses almost all the combinatorics of the poset. However in some favorable cases, part of the combinatorics is encoded in the Serre functor.

In this talk, I will present the combinatorics of the Serre functor of the Tamari lattice. This leads to a more algebraic proof of its fractional Calabi-Yau property. It is also the first step toward a generalization to a larger family of posets. 

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Junyang Liu Singularity categories via McKay quivers with potential 10/06/2024 14:00 zoom only

In 2018, Kalck and Yang showed that the singularity categories associated with 3-dimensional Gorenstein quotient singularities are triangle equivalent (up to direct summands) to small cluster categories associated with McKay quivers with potential. I introduce graded McKay quivers with potential and generalize Kalck-Yang's theorem to arbitrary dimensions. The singularity categories I consider occur as stable categories of categories of maximal Cohen-Macaulay modules. I refine my description of the singularity categories by showing that these categories of maximal Cohen-Macaulay modules are equivalent to Higgs categories in the sense of Wu. Moreover, I describe the singularity categories in the non-Gorenstein case. 

This talk will take place on Zoom only.

+ Matthew Pressland tba 17/06/2024 14:00 Info sur https://researchseminars.org/seminar/paris-algebra-seminar
+ Séances antérieures

Séances antérieures

Orateur(s)Titre Date DébutSalleAdresse
+ David Pauksztello Convex geometry for (co)fans of abelian categories 27/05/2024 14:00 IHP et Zoom

  Arising in cluster theory, the g-vector fan is a convex geometric invariant encoding the mutation behaviour of clusters. In representation theory, the g-vector fan encodes the mutation theory of support tau-tilting objects or, equivalently, two-term silting objects. In this talk, we will describe a generalisation of the g-vector fan which in some sense “completes” the g-vector fan: the heart fan of an abelian category. This convex geometric invariant encodes many important homological properties: e.g. one can detect from the convex geometry whether an abelian category is length, whether it has finitely many torsion pairs, and whether a given Happel-Reiten-Smaloe tilt is length. This talk will be a report on joint work with Nathan Broomhead, David Ploog and Jon Woolf.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Paul Wedrich tba 13/05/2024 14:00
+ Markus REINEKE Floer potentials, cluster algebras and quiver representations 06/05/2024 14:00

We interpret Floer potentials (encoding certain Gromov-Witten invariants) of "exotic" monotone Lagrangian tori in dle Pezzo surfaces as cluster characters of representations of certain quivers with potential.

This talk will be on Zoom only.

+ Marco Robalo Choices of HKR isomorphisms and exponential maps 29/04/2024 14:00 IHP et Zoom

In this talk, I will explain a computation describing the space of choices of functorial HKR isomorphisms as choices of exponential maps from the additive to the multiplicative formal group. This computation uses the construction of a filtered circle obtained in collaboration with with Moulinos and Toën, which combines the HKR filtration and the circle action on Hochschild homology even when the characteristic of the base field is positive. We will review the construction of the filtered circle and the relation with Witt vectors.

This talk will take place in hybrid mode at the Institut Henri Poincaré.


+ Tiago Cruz Relative Auslander-Gorenstein pairs 22/04/2024 14:00 IHP et Zoom

A famous result in representation theory is Auslander’s correspondence which connects finite-dimensional algebras of finite representation-type with Auslander algebras. Over the years, many generalisations of Auslander algebras have been proposed: for instance n-Auslander algebras (by Iyama), n-minimal Auslander–Gorenstein algebras (by Iyama and Solberg), among others. All of the concepts above require the existence of a faithful projective-injective module and use classical dominant dimension. Now replace the faithful projective-injective module with a self-orthogonal module and classical dominant dimension with relative dominant dimension with respect to a module and you get a relative Auslander-Gorenstein pair.

In this talk, we introduce relative Auslander-Gorenstein pairs. Further, we will characterise relative Auslander pairs (those whose underlying algebras have finite global dimension) by the existence and uniqueness of tilting-cotilting modules having the highest values of relative dominant and codominant dimension with respect to the self-orthogonal module. At the end, we discuss explicit examples of relative Auslander pairs. (This is joint work with Chrysostomos Psaroudakis.)

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Dmitriy Voloshyn Generalized cluster structures on the special linear group 08/04/2024 14:00 Zoom only

The Gekhtman-Shapiro-Vainshtein conjecture (the GSV conjecture) states that for any any given simple complex algebraic group G and any Poisson bracket from the Belavin-Drinfeld class, there exists a compatible generalized cluster structure. In this talk, I will review the process of constructing compatible generalized cluster structures, as well as the current state-of-the-art on the GSV conjecture. After that, I will describe a construction of generalized cluster structures on SL_n compatible with Poisson brackets induced from the Poisson dual of SL_n endowed with the Poisson structure determined by a BD triple of type A_{n-1}. I will also describe the associated family of birational quasi-isomorphisms. The talk will be based on the preprint arXiv:2312.04859 (joint work with M. Gekhtman). 

This talk will take place on Zoom only.

+ Hussein Mourtada Singularities of algebraic varieties and integer partitions 25/03/2024 14:00 IHP et Zoom

I will talk about a link between arc spaces of singularities, which are algebro-geometric objects, and identities of integer partitions. This link allows us to discover new partition identities in the spirit of the work of Ramanujan. The talk is accessible to a wide audience. 

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Nicholas WILLIAMS Donaldson-Thomas invariants for the Bridgeland-Smith correspondence 18/03/2024 14:00 IHP et Zoom

Celebrated work of Bridgeland and Smith shows a correspondence between quadratic differentials on Riemann surfaces and stability conditions on certain 3-Calabi--Yau triangulated categories. Part of this correspondence is that finite-length trajectories of the quadratic differential correspond to stable objects of phase 1. Speaking roughly, these stable objects are then counted by an associated Donaldson--Thomas invariant. Work of Iwaki and Kidwai predicts particular values for these Donaldson--Thomas invariants according to the different types of finite-length trajectories, based on the output of topological recursion. We show that the category recently studied by Christ, Haiden, and Qiu produces Donaldson--Thomas invariants matching these predictions. This is joint work with Omar Kidwai.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Sabin Cautis Categorical cluster structure of Coulomb branches 11/03/2024 14:00 IHP et Zoom

Coulomb branches are certain moduli spaces arising in supersymmetric field theory. They include as special cases many spaces of independent interest such as double affine Hecke algebras, certain open Richardson varieties, multiplicative Nakajima quiver varieties etc. In the four-dimensional case, one expects that their coordinate rings can be categorified by abelian monoidal categories carrying a cluster structure. After reviewing the mathematical construction of these Coulomb branches we will explain how these categories are constructed and why the cluster structure appears. This is joint work with Harold Williams. 


This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Merlin CHRIST Complexes of stable infinity-categories and perverse schobers 04/03/2024 14:00 IHP et Zoom

A complex of stable infinity-categories is a categorification of a chain complex, meaning a sequence of stable infinity-categories together with a differential that squares to the zero functor. Examples of such categorical complexes arise for instance via a categorification of the totalization construction, which produces a categorical complex from a categorical multi-complex, such as a commuting cube of stable infinity-categories. We will then explain how categorified perverse sheaves, also known as perverse schobers, on C^n (with a certain stratification) can be described in terms of categorical cubes and categorical complexes of spherical functors, and what categorical totalization means in this case geometrically. This talk is based on joint work with T. Dyckerhoff and T. Walde. 

This talk will take place in hybrid mode at the Institut Henri Poincaré.


+ Yu Qiu On cluster braid groups 26/02/2024 14:00 Zoom only

We introduce cluster braid groups, with motivations coming from the study of stability conditions on triangulated categories. In the Coxeter-Dynkin case, they are naturally isomorphic to the corresponding Artin braid groups (1407.5986 and 2310.02871). In the surface case, they are naturally isomorphic to braid twist groups (1407.0806, 1703.10053 and 1805.00030). If time permits, I will mention an application to quadratic differentials.

This talk will take place on Zoom only.

+ Geoffrey Janssens Group invariants observed through a representation-theoretical lens 12/02/2024 14:00 IHP et Zoom

The leitfaden of this talk will be the general problem of determining which invariants of a finite group G are determined by which piece of the representation category of G over a commutative ring R. In the first part of the talk, we will recall the information encoded by the monoidal category of complex representations and its (braided) auto-equivalences. By doing so we will stumble on a question concerning the connection between two types of rigidity associated to G. The first is given by the group of class-preserving outer automorphisms of G and the second is a birational invariant of the quotient variety V/G, where V is a faithful representation of G. The aim of the second part of the talk will be to present some new perspective on them. Thereafter, in the last part, we will explain how the situation changes when taking R to be a number field or its ring of integers. In particular, the role of the theory of arithmetic groups will be emphasized. All along the talk, we will mention some open questions and some recent contributions.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Xiaofa Chen Exact dg categories and higher Auslander correspondences 05/02/2024 14:00

Exact dg categories allow to enhance extriangulated categories and to perform constructions like functor categories or tensor products for which the extriangulated structure alone does not suffice. In particular, they yield a new approach to and a generalization of higher versions of Auslander correspondences as established by Iyama and by Iyama-Solberg, for example. In this talk, I will give an introduction to exact dg categories and sketch their application to correspondences on the example of 0-Auslander categories. We will see in particular that the framework of exact dg categories allows to enhance the correspondences to equivalences of infinity-groupoids.

This talk will take place on Zoom only.

+ Till Wehrhan Chevalley-Monk formulas for bow varieties 29/01/2024 14:00 IHP et Zoom

The theory of stable envelopes, introduced by Maulik and Okounkov, provides a fascinating interplay between the geometry of holomorphic symplectic varieties and integrable systems. We apply this theory to bow varieties which form a rich family of holomorphic symplectic varieties including type A Nakajima quiver varieties. We then discuss a formula for the multiplication of torus equivariant first Chern classes of tautological bundles of bow varieties with respect to the stable envelope basis. This formula naturally generalizes the classical Chevalley-Monk formula and can be expressed in terms of moves on skein-type diagrams that label the stable envelope basis. 

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Fan QIN Applications of the freezing operators on cluster algebras 22/01/2024 14:00 IHP et Zoom

We utilize freezing operators to establish connections among distinct (quantum) upper cluster algebras. This approach enables us to compare the quantized coordinate rings of different varieties. We prove that these operators send localized (quantum) cluster monomials to localized (quantum) cluster monomials. Furthermore, in many instances, they also preserve bases. Remarkably, the bases constructed via freezing operators coincide with those obtained via localization.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Johan Asplund Relative Ginzburg algebras and Chekanov-Eliashberg dg-algebras 15/01/2024 14:00 Zoom only

The Chekanov-Eliashberg dg-algebra yields a powerful isotopy invariant of (possibly singular) Legendrian submanifolds in a class of contact manifolds, and is also intimately related to Fukaya categories of a class of non-compact symplectic manifolds. The goal for this talk is to explain how the relative Ginzburg algebra associated to any ice quiver with trivial potential is quasi-isomorphic to some Chekanov-Eliashberg dg-algebra. The proof is constructive. I will give a gentle introduction to Chekanov-Eliashberg dg-algebras and will discuss how the relation to relative Ginzburg algebras is interesting to contact and symplectic geometers.

This talk will be on Zoom only.

+ Dirceu Bagio Tameness of a restricted enveloping algebra 08/01/2024 14:00 IHP et Zoom

 We will describe a 5-dimensional Lie algebra over an algebraically closed field of characteristic 2 and show that its restricted enveloping algebra is special biserial, hence tame. We obtain an explicit description of all of its families of finite-dimensional indecomposable modules using Crawley-Boevey's description via strings and bands of the indecomposable modules over a special biserial algebra. This is joint work with N. Andruskiewitsch, S. D. Flora and D. Flores.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Melissa Sherman-Bennett Cluster structures on braid and Richardson varieties 18/12/2023 14:00 Zoom only

 In 2014, Leclerc gave a construction of a conjectural cluster structure on open Richardson varieties in types ADE. His construction was categorical in nature, involving preprojective algebra modules. His conjecture inspired work on cluster structures on braid varieties in arbitrary type, which generalize open Richardsons. Two cluster structures on braid varieties were recently constructed. The first one, based on ideas and techniques from symplectic topology, is due to Casals-Gorsky-Gorsky-Le-Shen-Simental. I will discuss the other, which is joint work with Galashin, Lam and Speyer. Our main geometric tool is the Deodhar decomposition. In type A, our quivers are given by "3D plabic graphs", which generalize Postnikov's plabic graphs for the Grassmannian. Time permitting, I will also discuss related work with Serhiyenko, where we show that for type A Richardsons, Leclerc's conjectural categorical construction does in fact give a cluster structure, with quivers again given by 3D plabic graphs.

This talk will be on Zoom only.

+ JiaRui Fei Crystal Structure of Upper Cluster Algebras 11/12/2023 14:00 Zoom only

We describe the upper seminormal crystal structure for the μμ-supported δδ-vectors for any quiver with potential with reachable frozen vertices, or equivalently for the tropical points of the corresponding cluster XX-variety. We show that the crystal structure can be algebraically lifted to the generic basis of the upper cluster algebra. This can be viewed as an additive categorification of the crystal structure arising from cluster algebras. We introduce the biperfect bases and the strong biperfect bases in the cluster algebra setting and give a description of all strong biperfect bases.

This talk will be on Zoom only.

+ Jonah Berggren Consistent Dimer Models on Surfaces with Boundary 04/12/2023 14:00 Zoom only

A dimer model is a quiver with faces embedded in a surface. Dimer models on the disk and torus are particularly well-studied, though these theories have remained largely separate. Various “consistency conditions” may be imposed on dimer models on the disk or torus with implications relating to 3-Calabi-Yau properties and categorification. We extend many of these definitions and results to the setting of general surfaces with boundary. We show that the completed dimer algebra of a “strongly consistent” dimer model is bimodule internally 3-Calabi-Yau with respect to its boundary idempotent. As a consequence, the Gorenstein-projective module category of the completed boundary algebra of a suitable dimer model categorifies the cluster algebra given by its underlying ice quiver. We give a class of examples of annulus models satisfying the requisite conditions. 

This talk will take place on Zoom only.

+ Alexander Thomas A q-deformation of sl2 and the Witt algebra 27/11/2023 14:00 IHP et Zoom

I will present new q-deformations of Lie algebras linked to the modular group and the q-rational numbers as defined by Morier-Genoud and Ovsienko. In particular, I will describe deformations of sl2 and the Witt algebra. These deformations are realized as differential operators acting on the hyperbolic plane, giving new insights into q-rationals. 

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Wahei Hara Spherical objects in dimension two and three 20/11/2023 14:00 Zoom only

In this talk; we discuss the classification problem of spherical “like” objects in various geometric settings including the minimal resolution of an ADE surface singularity and a 3-fold flopping contraction. The classification of spherical objects is related to questions about the autoequivalence groups or Bridgeland stability conditions, but in 3-fold settings, this is not alway a correct problem to ask. In the first half of the talk, we discuss what kind of objects should be classified, and in the second half, a sketch of the proof will be explained. Our new technique can also be applied to the heart of a bounded t-structure, and classifies all t-structures of the associated null category. As a corollary, the connectedness of the space of stability conditions follows. This is all joint work with Michael Wemyss.

This talk will take place on Zoom only.

+ Luca Francone Minimal monomial lifting of cluster algebras and branching problems 13/11/2023 14:00 IHP et Zoom

The minimal monomial lifting is a sort of homogenisation technique, whose goal is to identify a cluster algebra structure on certain "suitable for lifting" schemes, compatibly with a base cluster structure on a distinguished subscheme. This technique allows to recover, by geometric methods, some well known cluster structures. In this talk, we will present this technique and discuss applications to branching problems in representation theory of complex reductive groups.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Merlin CHRIST Relative Calabi-Yau structures and extriangulated cluster categories 06/11/2023 14:00 IHP et Zoom

We will begin with an introduction to relative Calabi-Yau structures in the sense of Brav-Dyckerhoff, generalizing the notion of a Calabi-Yau triangulated (or dg-) category to functors. Via so-called relative theory, Calabi-Yau functors give rise to extriangulated categories, which are Frobenius 2-Calabi-Yau. We apply this to examples of cluster categories of surfaces, categorifying the surface cluster algebras with coefficients in the boundary arcs. This talk is mostly based on my preprint arXiv:2209.06595. 

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Norihiro Hanihara Silting-cluster tilting correspondences 23/10/2023 14:00 IHP et Zoom

Cluster categories are fundamental objects in representation theory, including such topics as cluster algebras, tilting theory, singularity theory. The theory of Amiot, Guo, and Keller shows that tilting/silting objects in derived categories (of a finite dimensional algebra or of a Calabi-Yau dg algebra) give rise to cluster tilting objects in the cluster category. We study such correspondences between silting objects and cluster tilting objects. We propose a conjecture on the liftability of cluster tilting objects in the cluster category to silting objects, and discuss some evidence for it. This is based on a joint work with Osamu Iyama.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Se-jin Oh A noncommutative algebra arising from the $t$-quantized Cartan matrix 16/10/2023 14:00 Zoom

The quantum Cartan matrix appears ubiquitously as a key combinatorial ingredient in the representation theory of quantum affine algebras. Through the generalized Schur-Weyl duality, it also plays a central role in the one of quiver Hecke algebras and the quantum unipotent coordinate ring of (skew-)symmetric finite type. Even though there are quiver Hecke algebras and quantum unipotent coordinate rings of non (skew-)symmetric finite type, there is no counterpart in representation theory as far as I and my collaborators understand. In this talk, I introduce a non-commutative ring over Q(q1/2Q(q1/2), which is expected to be a quantum Grothendieck ring for a Hernandez-Leclerc category, if such a representation theory exists, by using the t-quantized Cartan matrix. When we consider its heart subalgebra, the algebra is isomorphic to the quantum unipotent coordinate ring of any finite type. This talk is mainly based on joint work with Kashiwara, Jang and Lee.

This talk will take place on Zoom only.

+ Fan QIN Analogs of dual canonical bases for cluster algebras from Lie theory 09/10/2023 14:00 Zoom

The (quantized) coordinate rings of many interesting varieties from Lie theory are (quantum) cluster algebras. We construct the common triangular bases for these algebras. Such bases provide analogs of the dual canonical bases, whose existence has been long expected in cluster theory. For symmetric Cartan matrices, they are positive and admit monoidal categorification after base change. We employ a unified approach based on cluster algebra operations. Our results apply to algebraic groups, double Bott-Samelson cells, and braid varieties, etc. Additionally, we find applications in representations of quantum affine algebras.

This talk will take place on Zoom only.

+ Duncan Laurie Quantum toroidal algebras: braid group actions, automorphisms, and representation theory 02/10/2023 14:00 Zoom and IHP

Quantum toroidal algebras Uq(g_tor) occur as the Drinfeld quantum affinizations of quantum affine algebras. In particular; they contain (and are generated by) a horizontal and vertical copy of the affine quantum group. In type A, Miki obtained an automorphism of Uq(g_tor) exchanging these subalgebras, which has since played a crucial role in the investigation of its structure and representation theory.

In this talk; we shall construct an action of the extended double affine braid group B on the quantum toroidal algebra in all untwisted types. In the simply laced cases, using this action and certain involutions of B we obtain automorphisms and anti-automorphisms of Uq(g_tor) which exchange the horizontal and vertical subalgebras, thus generalising the results of Miki. We shall then discuss potential extensions of these results, and applications to the representation theory of quantum toroidal algebras.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Bill CRAWLEY-BOEVEY Integral representations of quivers 10/07/2023 14:00 Online

 In the 1990s, I classified rigid representations of a quiver by finitely generated free modules over a principal ideal ring. I shall extend the results to representations of a quiver by finitely generated projective modules over an arbitrary commutative ring.

This talk will kindly be shared by the organisation of the conference
Homological algebra and representation theory, cf.

+ Manuel Rivera Loop spaces and bialgebras 26/06/2023 14:00 IHP

I will discuss several interlocked constructions giving rise to bialgebra structures all of which have parallel algebraic and topological interpretations. The bialgebras considered will be of different flavors depending on the compatibility between the product and coproduct; for instance, we will see examples of Hopf, Frobenius, infinitesimal and Lie bialgebras. These structures appear when analyzing the role of loop spaces in homotopy theory and manifold topology and reveal new results regarding the algebraic nature of geometric space.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Frédéric CHAPOTON Posets and fractional Calabi-Yau categories 19/06/2023 14:00 IHP

In combinatorics, several famous enumeration results involve a special kind of product formula. The very same kind of product formula gives the Milnor number of an isolated quasi-homogenous singularity. It seems possible that one could relate combinatorics and singularities by means of derived categories: on the one hand, modules over incidence algebras of partially ordered sets (posets) and on the other hand, some kind of Fukaya-like category that should categorify the Milnor fibration. Even if part of this remains very unprecise and vague, this implies many concrete conjectures about derived equivalences between posets.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Antoine De Saint Germain Cluster additive functions and acyclic cluster algebras 12/06/2023 14:00 IHP

In his study of combinatorial features of cluster categories and cluster-tilted algebras, Ringel introduced an analogue of additive functions of stable translation quivers called cluster-additive functions.
In this talk, we will define cluster-additive functions associated to any acyclic mutation matrix, relate them to tropical points of the cluster X-variety, and realise their values as certain compatibility degrees between functions on the cluster A-variety associated to the Langlands dual mutation matrix (in accordance with the philosophy of Fock-Goncharov). This is based on joint work with Peigen Cao and Jiang-Hua Lu.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Lauren WILLIAMS The amplituhedron and cluster algebras 05/06/2023 14:00 IHP

I will give a gentle introduction to the amplituhedron, a geometric object that was introduced in the context of scattering amplitudes in N=4 super Yang Mills. I'll then explain some of the connections of the amplituhedron to cluster algebras.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Leonid Positselski The homomorphism removal and repackaging construction 22/05/2023 14:15 Online

This work is an attempt to understand the maximal natural generality context for the Koenig-Kuelshammer-Ovsienko construction in the theory of quasi-hereditary algebras by putting it into a category-theoretic context. Given a field k and a k-linear exact category E with a chosen set of nonzero objects F_i such that every object of E is a finitely iterated extension of some F_i, we construct a coalgebra C whose irreducible comodules L_i are indexed by the same indexing set, and an exact functor from C-comod to E taking L_i to F_i such that the spaces Ext^n between L_i in C−comod are the same as between F_i in E (for n > 0). Thus, the abelian category C−comod is obtained from the exact category E by removing all the nontrivial homomorphisms between the chosen objects F_i in E while keeping the Ext spaces unchanged. The removed homomorphisms are then repackaged into a semialgebra S over C such that the exact category E can be recovered as the category of S-semimodules induced from finite-dimensional C-comodules. The construction used Koszul duality twice: once as absolute and once as relative Koszul duality.

Talk shared by the GAP conference, cfhttps://personal.psu.edu/mps16/hirsutes2023/gap2023.html

You can follow the talk using the link (without interaction): https://www.ihp.fr/fr/live-0

+ Haibo Jin A complete derived invariant and silting theory for graded gentle algebras 15/05/2023 14:00 IHP

We show that among the derived equivalent classes of homologically smooth and proper graded gentle algebras there is only one class whose perfect derived category does not admit silting objects.

As one application  we give a sufficient and necessary condition for any homologically smooth and proper graded gentle algebra under which all pre-silting objects in its perfect derived category may be complete into silting objects.
As another application we confirm a conjecture by Lekili and Polishchuk that the geometric invariants which they construct for homologically smooth and proper graded gentle algebras are a complete derived invariant. Hence, we obtain a complete invariant for partially wrapped Fukaya categories of surfaces with stops.
This is a report on joint work with Sibylle Schroll and Zhengfang Wang.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Mikhail Bershtein Cluster Hamiltonian reductions: examples 08/05/2023 14:00 Online

I will talk about an, in general conjectural, construction of a X-cluster structure on
certain Hamiltonian reductions of an X-cluster variety. There are two main classes of examples of
such constructions: moduli spaces of framed local systems with special monodromies and phase spaces of
Goncharov-Kenyon integrable systems. The first class includes the phase space of open XXZ chain and
Ruijsenaars integrable systems. The second class includes integrable systems corresponding to the
q-difference Painleve equations.
Based on works in progress and discussions with P. Gavrylenko, A. Marshakov, M. Semenyakin,
A. Shapiro, G. Schrader.

This talk will take place on Zoom only.

+ Owen Garnier Homology of a category and the Dehornoy-Lafont order complex 24/04/2023 14:00 IHP

The work of Squier and Kobayashi proves that the homology of a monoid can be computed using a so called complete rewriting system, which acts as a convenient presentation of the monoid. Later, Dehornoy and Lafont noted that such a convenient presentation arises in particular when considering monoids satisfying combinatorial assumptions regarding existence of lcms. This gave rise to the so called Dehornoy-Lafont order complex, which was used to compute the homology of complex braid groups by Callegaro and Marin. After giving a quick summary of these works, I will present a generalization of this latter complex to the case of a category which again satisfies convenient combinatorial assumptions. Of course, as my "true" goal is to compute the homology of a group using some associated category, I will also give a link between the homology of a category, that of its enveloping groupoid, and that of a group which is equivalent to the said groupoid. Lastly, I will explain an application to the case of the complex braid group B31B31​, which is studied through its associated Garside category, and which was not directly covered by previous approaches.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

+ Eric VASSEROT Critical convolution algebras and quantum loop groups 17/04/2023 14:00 IHP

 We introduce a new family of algebras attached to quivers with potentials, using critical K-theory and critical Borel-Moore homology. They generalize the convolution algebras attached to quivers by Nakajima. We give some applications to cohomological and K-theoretical Hall algebras, to shifted quantum loop groups, and to Kirillov-Reshetikhin and prefundamental representations.

This talk will take place in hybrid mode at the IHP.

+ Amnon YEKUTIELI An Algebraic Approach to the Cotangent Complex 03/04/2023 14:00

Let $B/A$ be a pair of commutative rings. We propose an algebraic approach to the cotangent complex $L_{B/A}$. Using commutative semi-free DG ring resolutions of B relative to A, we construct a complex of $B$-modules $LCot_{B/A}$. This construction works more generally for a pair $B/A$ of commutative DG rings. In the talk, we will explain all these concepts. Then we will discuss the important properties of the DG $B$-module $LCot_{B/A}$. It time permits, we'll outline some of the proofs. It is conjectured that for a pair of rings $B/A$, our $LCot_{B/A}$ coincides with the usual cotangent complex $L_{B/A}$, which is constructed by simplicial methods. We shall also relate $LCot_{B/A}$ to modern homotopical versions of the cotangent complex.

+ Gleb KOSHEVOY Polyhedral parametrization of canonical bases 27/03/2023 14:00 IHP

 Parametrizations of the  canonical bases, string basis and theta basis, can be obtained by the tropicalization of  the Berenstein-Kazhdan decoration function and the Gross-Hacking-Keel-Kontsevich potential respectively. For  a classical Lie algebra and a reduced decomposition $\mathbf i$,  the decorated graphs are constructed algorithmically, vertices of such graphs are labeled by monomials which constitute the set of monomials of the Berenstein-Kazhdan potential.  Due to this algorithm;  we obtain a characterization of $\mathbf i$-trails introduced by Berenstein and Zelevinsky. Our algorithm uses multiplication and summations only, its complexity is linear in time of writing the monomials of the potential. For SL_n, there is an algorithm due to Gleizer and Postnikov which gets all monomials of the Berenstein-Kazhdan potential using combinatorics of wiring diagrams. For this case, our algorithm uses simpler combinatorics and is faster than the Gleizer-Postnikov algorithm. The cluster algorithm due to Genz, Schumann and me is polynomial in time but it uses divisions of polynomials of several variables.
If time permits, I will report on applications of decorated graphs to analysis of the Newton polytopes of F-polynomials related to the Gross-Hacking-Keel-Kontsevich potentials. The talk is based on joint works with Volker Genz and Bea Schumann and with Yuki Kanakubo and Toshiki Nakashima.

The talk will take place in hybrid mode at the Institut Henri Poincaré

+ Markus REINEKE Expander representations 20/03/2023 14:00 IHP

Dimension expanders, introduced by Wigderson and Lubotzky-Zelmanov, are a linear algebra analogue of the notion of expander graphs. We interpret this notion in terms of quiver representations, as a quantitative variant of stability. We use Schofield’s recursive description of general subrepresentations to re-derive existence of dimension expanders and to determine optimal expansion coefficients.

The talk will take place in hybrid mode at the Institut Henri Poincaré

+ Julian Holstein Enriched Koszul duality for dg categories 13/03/2023 14:00 Sophie Germain

The category of dg categories is related by Koszul duality to a certain category of colagebras, so-called pointed curved coalgebras. In this talk we wil review this Quillen equivalence and observe that it is in fact quasi-monoidal. By constructing internal homs of pointed curved coalgebras we can then construct a concrete closed monoidal model for dg categories. In particular this gives natural descriptions of mapping spaces and internal homs between dg categories. This is joint work with A. Lazarev.

Exceptionally, this talk will take place in hybrid mode in room 1013 of the Sophie Germain building (8, place Aurélie Nemours, 75013 Paris).

+ Luc PIRIO Hyperlogarithmic functional identities on del Pezzo surfaces 06/03/2023 14:00 Sophie Germain

For any d in {1,…,6}, we prove that the web of conics on a del Pezzo surface of degree d carries a functional identity HLog(7-d) whose components are antisymmetric hyperlogarithms of weight 7-d. Our approach is uniform with respect to d and relies on classical results about the action of the Weyl group on the set of lines on the del Pezzo surface. These hyperlogarithmic functional identities HLog(7-d) are natural generalizations of the classical 3-term and (Abel's) 5-term identities of the logarithm and the dilogarithm, which are the identities HLog(1) and HLog(2) corresponding to the cases d=6 and d=5 respectively.
If time allows, I will give a list of many nice properties enjoyed by the 5-term identity of the dilogarithm and will explain that most of these properties (such as being of cluster type) have natural generalizations which are satisfied by the weight 3 hyperlogarithmic identity HLog(3).
The talk will be mainly based on the preprint arXiv:2301.06775 written with Ana-Maria Castravet.

Exceptionally, this talk will take place in hybrid mode in room 1013 of the Sophie Germain building (8, place Aurélie Nemours, 75013 Paris).

+ Haruhisa Enomoto Maximal self-orthogonal modules and a new generalization of tilting modules 27/02/2023 14:00

We study self-orthogonal modules, i.e., modules T such that Ext^i(T, T) = 0 for all i > 0. We introduce projectively Wakamatsu-tilting modules (pW-tilting modules) as a generalization of tilting modules. If A is a representation-finite algebra, every self-orthogonal A-module can be completed to a pW-tilting module, and the following classes coincide: pW-tilting modules, Wakamatsu tilting modules, maximal self-orthogonal modules, and self-orthogonal modules T with |T| = |A|. We also prove that every self-orthogonal module over a representation-finite Iwanaga-Gorenstein algebra has finite projective dimension. We finally explain some open conjectures on self-orthogonal modules.

+ Fan QIN Bracelets are theta functions for surface cluster algebras 20/02/2023 14:00

The skein algebra of a marked surface admits the basis of bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-Williams. As a cluster algebra, it also admits the theta basis from the cluster scattering diagram by Gross-Hacking-Keel-Kontsevich. In a joint work with Travis Mandel, we show that the two bases coincide except for the once-punctured torus. Our results extend to quantum cluster algebras with coefficients arising from the surface even in punctured cases. Long-standing conjectures on strong positivity and atomicity follow as corollaries.

Exceptionally, this talk will take place in hybrid mode in room 1013 of the Sophie Germain building (8, place Aurélie Nemours, 75013 Paris).

+ Willie Liu Translation functors for trigonometric double affine Hecke algebras 13/02/2023 14:00 Zoom

The double affine Hecke algebra was introduced by Cherednik around 1995 as a tool in his study of Macdonald polynomials. Its degenerate version, called trigonometric double affine Hecke algebra (TDAHA), has also turned out to be linked to different areas, notably to the representation theory of pp-adic groups. Given a root system, the TDAHA HcHc​ depends on a family of complex parameters cc. Given two families of parameters cc and c′c′ whose difference takes integer values, there exists a triangle equivalence between the bounded derived categories of the corresponding TDAHAs, which we call translation functor. The objective of this talk is to explain the construction of this functor. 

This talk will be on Zoom only.

+ Keyu Wang QQ˜ -systems for twisted quantum affine algebras 06/02/2023 14:00 IHP

Abstract: As a part of Langlands duality, certain equations were found in two different areas of mathematics. They are known as Baxter’s TQ systems and the QQ type systems, as they trace back to Baxter’s study on integrable models in the 1970s. During the same decade, similar systems of equations were discovered in the area of ordinary differential equations (ODE) by Sibuya, Voros and others. Today, this remarkable correspondence is realized as a duality between representation theory of nontwisted quantum affine algebras (QAA) and the theory of opers for their Langlands dual Lie algebras.
We are interested in this duality when the roles of the affine Lie algebra and its dual are exchanged. When the nontwisted QAA is of type BCFG, its dual will be a twisted QAA. To exchange their roles amounts to studying representations of twisted QAAs.
In this talk, we will begin by reviewing this story. We will explain the representation theory of twisted QAAs and their Borel algebras. We will explain the expected relationship between twisted and nontwisted types, and we will establish TQ systems and QQ^{~} systems for twisted QAAs.

This talk will take place in hybrid mode at the IHP.

+ Edmund Heng Coxeter quiver representations in fusion categories and Gabriel’s theorem 30/01/2023 14:00 IHP

One of the most celebrated theorems in the theory of quiver representations is undoubtedly Gabriel’s theorem, which reveals a deep connection between quiver representations and root systems arising from Lie algebras. In particular, Gabriel’s theorem shows that the finite-type quivers are classified by the ADE Dynkin diagrams and the indecomposable representations are in bijection with the underlying positive roots. Following the works of Dlab—Ringel, the classification can be generalised to include all the other Dynkin diagrams (including BCFG) if one considers the more general notion of valued quivers (K-species) representations instead.

While the theories above relate (valued) quiver representations to root systems arising from Lie algebras, the aim of this talk is to generalise Gabriel’s theorem in a slightly different direction using root systems arising in Coxeter theory. Namely, we shall introduce a new notion of Coxeter quivers and their representations built in (other) fusion categories, where we have a generalised Gabriel’s theorem as follows: a Coxeter quiver has finitely many indecomposable representations if and only if its underlying graph is a Coxeter-Dynkin diagram — including the non-crystallographic types H and I. Using a similar notion of reflection functors as introduced by Bernstein—Gelfand—Ponomarev, we shall also show that the isomorphism classes of indecomposable representations of a Coxeter quiver are in bijection with the positive roots associated to the root system of the underlying Coxeter graph. --

This talk will take place in hybrid mode at the IHP.

+ Duc-Khanh Nguyen A generalization of the Murnaghan-Nakayama rule for $K$-$k$-Schur and $k$-Schur functions 23/01/2023 14:00

We introduce a generalization of $K$-$k$-Schur functions and k-Schur functions via the Pieri rule. Then we obtain the Murnaghan-Nakayama rule for the generalized functions. The rule is described explicitly in the cases of $K$-$k$-Schur functions and $k$-Schur functions, with concrete descriptions and algorithms for coefficients. Our work recovers the result of Bandlow, Schilling, and Zabrocki for $k$-Schur functions, and explains it as a degeneration of the rule for $K$-$k$-Schur functions. In particular, many other special cases promise to be detailed in the future.

+ Alireza Nasr-Isfahani Lower bound cluster algebras generated by projective cluster variables 16/01/2023 14:00

We introduce the notion of a lower (upper) bound cluster algebra generated by projective cluster variables. Projective cluster variables are often categorified by projective modules of the corresponding quiver with relations. We show that under an acyclicity assumption, the cluster algebra and the lower bound cluster algebra generated by projective cluster variables coincide. In this case, we use our results to construct a basis for the cluster algebra. We also show that the coincidence between cluster algebra and the lower bound cluster algebra generated by projective cluster variables holds beyond acyclic seeds. Part of this talk is based on joint work with Karin Baur.

+ Raphaël ROUQUIER Coherent realizations of 2-representations 12/12/2022 14:00 shared talk

2-representations of Kac-Moody algebras arise algebraically and as categories of constructible sheaves. We will discuss two settings involving coherent sheaves: derived cotangent bundles to spaces of quiver representations and spaces of quasi-maps in flag varieties.
This talk will be shared by the conference "Geometric representation theory and quantum topology", cf. http://georep22.imj-prg.fr/

+ Euiyong PARK Extended crystal structures of Hernandez-Leclerc categories 05/12/2022 14:00

In this talk, we talk about the categorical crystal structure on the Hernandez-Leclerc category $\mathscr{C}_\mathfrak{g}^0$. We define extended crystals for quantum groups and show that there is a braid group action on extended crystals.  We then explain how the set of the isomorphism classes of simple modules in $\mathscr{C}_\mathfrak{g}^0$ has an extended crystal structure, and discuss the braid group action from the viewpoint of the Hernandez-Leclerc category $\mathscr{C}_\mathfrak{g}^0$. This talk is based on a joint work with M. Kashiwara (arXiv: 2111.07255 and 2207.11644).

+ Fernando Muro and Gustavo Jasso The triangulated Auslander-Iyama correspondence, II 28/11/2022 14:00

In these two talks, we will start by introducing a result which establishes the existence and uniqueness of (DG) enhancements for triangulated categories which admit an additive generator whose endomorphism algebra is finite-dimensional (over a perfect field). We will then present a generalisation of this result that allows us to treat a larger class of triangulated categories, which instead admit a generator with a strong regularity property (a so-called dZ-cluster tilting object). We will also explain how our result, combined with crucial theorems of August and Hua-Keller, leads to a positive solution of the Donovan-Wemyss Conjecture for contraction algebras as observed by Keller. We will also comment on some details about the proof.

+ Gustavo Jasso and Fernando Muro The triangulated Auslander-Iyama correspondence, I 21/11/2022 14:00

In these two talks, we will start by introducing a result which establishes the existence and uniqueness of (DG) enhancements for triangulated categories which admit an additive generator whose endomorphism algebra is finite-dimensional (over a perfect field). We will then present a generalisation of this result that allows us to treat a larger class of triangulated categories, which instead admit a generator with a strong regularity property (a so-called dZ-cluster tilting object). We will also explain how our result, combined with crucial theorems of August and Hua-Keller, leads to a positive solution of the Donovan-Wemyss Conjecture for contraction algebras as observed by Keller. We will also comment on some details about the proof.

+ Ivan Marin Geometric realization via random variables 14/11/2022 14:00

Topological spaces up to (weak) equivalences are faithfully represented by simplicial combinatorial structures. Through an identification of the $n$-dimensional simplex with the space of probability measures on a finite set of size $n+1$, we investigate what happens when it is replaced by the space of random variables that naturally lies 'above' it. By this procedure, we obtain in particular a simple description of the classifying set of a (discrete) group, and also a new concept of geometric realization. This new one also induces an equivalence of categories up to homotopy with simplicial sets and topological spaces. The 'probability-law' map then defines a natural transformation between the two corresponding Quillen equivalences.

+ Daniel LABARDINI-FRAGOSO Revisiting Derksen-Weyman-Zelevinsky's mutations 07/11/2022 14:00 Talk in person at IHP and broadcasted via Zoom

The mutation theory of quivers with potential and their representations, developed around 15 years ago by Derksen-Weyman-Zelevinsky, has had a profound impact both inside and outside the theory of cluster algebras. In this talk I will present results obtained in joint works with Geiss and Schröer, and with de Laporte, about some interesting behaviors of DWZ's mutations of representations. Namely, despite needing several non-canonical choices of linear-algebraic data in order to be performed, they can always be arranged so as to become regular maps on dense open subsets of representation spaces rep(Q,S,d). As a consequence, one obtains the invariance of Geiss-Leclerc-Schröer's 'generic basis' under mutations even in the Jacobi-infinite case, thus generalizing a result of Plamondon. Furthermore, given two distinct vertices k, \ell of a quiver with potential (Q,S), the k-th mutation of representations takes the \ell-th indecomposable projective over (Q,S) to the \ell-th indecomposable projective over \mu_k(Q,S). When a certain 'optimization' condition is satisfied by \ell, this allows to compute certain 'Landau-Ginzburg potentials' as F-polynomials of projective representations.

+ Sota Asai TF equivalence classes and canonical decompositions for E-tame algebras 31/10/2022 14:00

This is joint work with Osamu Iyama. Let $A$ be a finite dimensional algebra over an algebraically closed field. Then the numerical torsion pairs of Baumann-Kamnitzer-Tingley give an equivalence relation on the real Grothendieck group of finitely generated projective $A$-modules, which is called TF equivalence. By results of Yurikusa and Bruestle-Smith-Treffinger, we have that the g-vector cone of each 2-term presilting complex is a TF equivalence class. To get more TF equivalence classes, we can use canonical decompositions of elements in the (integral) Grothendieck group of finitely generated projectives introduced by Derksen-Fei. We have showed that the cone defined by the canonical decomposition of each element is contained in some single TF equivalence class. Moreover, we have also obtained that, if $A$ is an E-tame algebra, then this cone is precisely a TF equivalence class. In this talk, I will explain these results and some important steps to prove them.

+ Julia Sauter Tilting theory in exact categories 24/10/2022 14:00

We define tilting subcategories in arbitrary exact categories to archieve the following. Firstly: Unify existing definitions of tilting subcategories to arbitrary exact categories. Discuss standard results for tilting subcategories: Auslander correspondence, Bazzoni description of the perpendicular category. Secondly: We treat the question of induced derived equivalences separately - given a tilting subcategory T, we ask if a functor on the perpendicular category induces a derived equivalence to a (certain) functor category over T. If this is the case, we call the tilting subcategory ideq tilting. We prove a generalization of Miyashita's theorem (which is itself a generalization of a well-known theorem of Brenner-Butler) and characterize exact categories with enough projectives allowing ideq tilting subcategories. In particular, this is always fulfilled if the exact category is abelian with enough projectives.

+ Linhui Shen Cluster Nature of Quantum Groups 17/10/2022 14:00

We present a rigid cluster model to realize the quantum group U_q(g) for g of type ADE. That is, we prove that there is a natural Hopf algebra isomorphism from the quantum group to a quotient algebra of the Weyl group invariants of a Fock-Goncharov quantum cluster algebra. By applying the quantum duality of cluster algebras, we show that the quantum group admits a cluster canonical basis Theta whose structural coefficients are in Laurent polynomials with non negative integer coefficients in the square root of q. The basis Theta satisfies an invariance property under Lusztig's braid group action, the Dynkin automorphisms, and the star anti-involution.

+ Greg Muller Juggler's friezes 10/10/2022 14:00

Frieze patterns are infinite strips of numbers satisfying certain determinantal identities. Originally motivated by Gauss’ “miraculous pentagram” identities, these patterns have since been connected to triangulations, integrable systems, representation theory, and cluster algebras. In this talk, we will review a few characterizations and constructions of frieze patterns, as well as a generalization which allows friezes with a “ragged edge” described by a juggling function. These “juggler’s friezes” correspond to special points in positroid varieties, in direct analogy with how classical friezes correspond to special points in Grassmannians.

+ Slava Pimenov Planar Prop of Differential Operators of Associative Algebras 03/10/2022 14:00
+ Amnon Neeman Two results, both developments of a 2015 article by Krause 26/09/2022 14:00

In 2020, the pandemic hit, and all around the globe we went into lockdowns of various description. During the first lockdown I carefully read Krause's 2015 article "Deriving Auslander's formula". In this talk, I will outline how the ideas of Krause's paper underpin two articles written in 2020 in collaboration with Canonaco and Stellari. One is about the uniqueness of enhancements of large classes of triangulated categories, while the second offers a counterexample to certain vanishing conjectures in negative K-theory. [This zoom talk is kindly shared by Representation theory and triangulated categories.]

+ Mikhail Kapranov Perverse sheaves and schobers on symmetric products 12/09/2022 14:00

The talk, based on joint work in progress with V. Schechtman, will first
recall our description of perverse sheaves on $Sym^n(\mathbb{C})$, the symmetric
product of the complex line with its natural stratification by multiplicities.
This description proceeds in terms of contingency matrices, which are certain
integer matrices appearing (besides their origin in statistics) in three
different contexts:
-- A natural cell decomposition of $Sym^n(\mathbb{C})$.
-- Compatibility of multiplication and comultiplication in $\mathbb{Z}_+$-graded Hopf algebras.
-- Parabolic Bruhat decomposition for $GL_n$.
Perverse sheaves on $Sym^n(\mathbb{C})$ are described in terms of certain data
of mixed functoriality on contingency matrices which we call Janus sheaves.
I will then explain our approach to categorifying the concept of Janus sheaves,
in which sums are replaced by filtrations with respect to the Bruhat order.
Such data can be called Janus schobers. Examples can be obtained from
$\mathbb{Z}_+$-graded Hopf categories, a concept going back to Crane-Frenkel,
of which we consider two examples related to representations of groups $GL_n$
over finite fields (Joyal-Street) and $p$-adic fields (Bernstein-Zelevinsky).
(Zoom talk shared with https://nc-shapes.info )

+ Sibylle Schroll Recollements of derived categories of graded gentle algebras 04/07/2022 14:00

Graded gentle algebras are classical objects in representation theory. They are quadratic monomial algebras making them particularly amenable to study and they appear in many different areas of mathematics such as in cluster theory, in N=2 gauge theories and in homological mirror symmetry of surfaces. In this talk, we give a construction of a partial cofibrant dg algebra resolution of a graded quadratic monomial algebra inducing an explicit recollement of their derived categories. We show that for graded gentle algebras, both the left and the right side of such a recollement corresponds to cutting the underlying surface which can be associated to a graded gentle algebra. In the case of homologically smooth and proper graded gentle algebras this recollement can be restricted to the derived categories with finite total cohomology, thus inducing a recollement of the corresponding partially wrapped Fukaya categories. We give some consequences of this construction such as the existence of full exceptional sequences, silting objects and simple minded collections. This is joint work with Wen Chang and Haibo Jin arxiv.org/abs/2206.11196.

+ Daping Weng Grid plabic graphs, Legendrian weaves, and (quasi-)cluster structures 27/06/2022 14:00

Given a plabic graph on R^2, we can choose a conormal lift of its zig-zag strands to the unit cotangent bundle of R^2, obtaining a Legendrian link. If the plabic graph satisfies a “grid” condition, its Legendrian link admits a natural embedding into the standard contact R^3. We study the Kashiwara-Schapira moduli space of microlocal rank 1 sheaves associated with the Legendrian link, and construct a natural (quasi-)cluster structure on this moduli space using Legendrian weaves. In particular, we prove that any braid variety associated with (beta Delta) for a 3-strand braid beta admits cluster structures with an explicit construction of initial seeds. We also construct Donaldson-Thomas transformations for these moduli spaces and prove that the upper cluster algebra equals its cluster algebra. In this talk, I will introduce the theoretical background and describe the basic combinatorics for constructing Legendrian weaves and the (quasi-)cluster structures from a grid plabic graph. This is based on joint work with Roger Casals, cf. arxiv.org/abs/2204.13244.

+ Alexander Shapiro Positive representation theory 20/06/2022 14:00

The notions of a modular tensor category, 2d topological modular functor, and 3d topological quantum field theory are essentially equivalent. Fock and Goncharov conjectured that the quantised higher Teichmüller theory gives rise to an analogue of a modular functor. Their construction in turn yields a family of "positive" representations of quantum groups. I will argue that these representations provide a compelling first step towards constructing an analogue of a modular tensor category. This talk will be based on joint works with Gus Schrader.

+ Yuya Mizuno g-simplicial complex and silting theory 13/06/2022 14:00

 For a finite dimensional algebra A, the 2-term silting complexes of A give a simplicial complex \( \Delta(A)\), which is called the g-simplicial complex.
We study several properties of \( \Delta(A)\) and, in particular, we give tilting theoretic interpretations of the h-vectors and the Dehn-Sommerville equations of  \( \Delta(A)\).Consequently, we can explain a close correspondence between torsion classes and wide subcategories, which can be regarded as a refinement of the Koenig-Yang correspondence. This is joint work with Aoki-Higashitani-Iyama-Kase, cf. arxiv.org/pdf/2203.15213.pdf

+ Jeremy RICKARD Generating the derived category 06/06/2022 14:00

The unbounded derived category of (right) modules over a ring is a triangulated category with infinite products and coproducts. As a triangulated category with coproducts it is easy to see that it is generated by the projective modules, and similarly it is generated as a triangulated category with products by the injective modules. I will discuss the question of whether it is generated as a triangulated category with coproducts by the injective modules, or as a triangulated category with products by the projective (or flat) modules. I will describe the relationship with the finitistic dimension conjecture, as well as some more recent results.

+ Jens Niklas Eberhardt Motivic Springer Theory 30/05/2022 14:00

Algebras and their representations can often be constructed geometrically in terms of convolution of cycles. For example, the Springer correspondence describes how irreducible representations of a Weyl group can be realised in terms of a convolution action on the vector spaces of irreducible components of Springer fibers. Similar situations yield the affine Hecke algebra, quiver Hecke algebra (KLR algebra), quiver Schur algebra or Soergel bimodules. In this spirit, we show that these algebras and their representations can be realised in terms of certain equivariant motivic sheaves called Springer motives. On our way, we will discuss weight structures and their applications to motives. This is joint work with Catharina Stroppel.

+ Bruno VALLETTE Pre-Calabi-Yau algebras and homotopy double Poisson algebras 23/05/2022 14:00

We prove that the notion of a curved pre-Calabi–Yau algebra is equivalent to the notion of a curved homotopy double Poisson gebra, thereby settling the equivalence between the two ways to define derived noncommutative Poisson structures. We actually prove that the respective differential graded Lie algebras controlling both deformation theories are isomorphic. This allows us to apply the recent developments of the properadic calculus in order to establish the homotopical properties of curved pre-Calabi–Yau algebras: infini-morphisms, homotopy transfer theorem, formality, Koszul hierarchy, and twisting procedure. (Joint work with Johan Leray available at arxiv.org/abs/2203.05062).

+ Thomas Bitoun On centralizers in Azumaya domains 16/05/2022 14:00

We prove a positive characteristic analogue of the classical result that the centralizer of a nonconstant differential operator in one variable is commutative. This leads to a new, short proof of that classical characteristic zero result, by reduction modulo p. This is joint work with Justin Desrochers available at arxiv.org/abs/2201.04606.

+ Florian Naef The (non-)homotopy invariance of the string coproduct 09/05/2022 14:00

A Calabi-Yau structure on a smooth algebra allows one to identify Hochschild homology with Hochschild cohomology. With this identification Hochschild homology acquires an additional Gerstenhaber algebra structure. One way to formulate the amount of structure one has on Hochschild homology is to encode it into a 2d TFT. This explains some of the string topology operations on the free loop space of a manifold, but not the string coproduct. If the algebra has additional structure (trivialization of its Hattori-Stalling Euler characteristic) one obtains an extra secondary operation on Hochschild homology, which recovers the string coproduct. Finally, in the free loop space setting, this additional structure can either be recovered from intersection theory of the manifold or from its underlying simple homotopy type, thus relating the two. Using this last relation one can express the difference between the string coproduct of two homotopic but not necessarily homeomorphic manifolds in terms of Whitehead torsion.
This is joint work with Pavel Safronov

+ Tasuki Kinjo Deformed Calabi--Yau completion and its application to DT theory 02/05/2022 14:00

In this talk, we investigate an application of the theory of deformed Calabi--Yau completion to enumerative geometry. The notion of Calabi--Yau completion was first introduced by Keller as a non-commutative analogue of the canonical bundle. In the same paper, he also introduced a deformed version of the Calabi--Yau completion. We will explain that the deformed Calabi--Yau completion is a non-commutative analogue of an affine bundle modeled on the canonical bundle. Combining this observation with a recent work of Bozec--Calaque--Scherotzke, we prove that the moduli space of coherent sheaves on a certain non-compact Calabi--Yau threefold is described as the critical locus inside a smooth moduli space. This description has several applications in Donaldson--Thomas theory including Toda's \chi-independence conjecture of Gopakumar--Vafa invariants for arbitrary local curves. By dimensional reduction, it implies (and extends) Hausel--Thaddeus's cohomological \chi-independence conjecture for Higgs bundles.This talk is based on a joint work with Naruki Masuda and another joint work with Naoki Koseki.

+ Léa Bittman A Schur-Weyl duality between Double Affine Hecke Algebras and quantum groups 25/04/2022 14:00

Schur-Weyl duality is often used to relate type A Lie groups (or quantum groups) to symmetric groups (or Hecke algebras). In this talk, I will use ribbon calculus and skein modules to describe an instance of this Schur-Weyl duality between representations of the type A quantum group at roots of unity and representations of the Double Affine Hecke Algebra. This is based on joint work with A. Chandler, A. Mellit and C. Novarini.

+ Peigen Cao On exchange matrices from string diagrams 11/04/2022 14:00

In this talk, we will first recall the constructions of triangular extension and of source-sink extensio for skew-symmetrizable matrices and some invariants under these constructions. Secondly, we will recall the string diagrams introduced by Shen-Weng, which are very useful to describe many interesting skew-symmetrizable matrices closely related with Lie theory. Thirdly, we will sketch the proof of our main result: the skew-symmetrizable matrices from string diagrams are in the smallest class of skew-symmetrizable matrices containing the (1 times 1) zero matrix and closed under mutations and source-sink extensions. This result applies to the exchange matrices of cluster algebras from double Bruhat cells, unipotent cells, double Bott-Samelson cells among others. Finally, some immediate applications regarding reddening sequences and non-degenerate potentials for many quivers from Lie theory are given.

+ Hipolito Treffinger Torsion classes and tau-tilting in higher homological algebra, I 04/04/2022 14:00

Higher homological algebra was introduced by Iyama in the late 2000's. His point-of-view was that some classical results by Auslander and Auslander--Reiten were somehow 2-dimensional and should have n-dimensional equivalents. This new theory quickly attracted a lot of attention, with many authors generalising classical notions to the setting of higher homological algebra. Examples of such generalisations are the introduction of n-abelian categories by Jasso, n-angulated categories by Geiss--Keller--Oppermann, and n-torsion classes by Jørgensen.Recently, it was shown by Kvamme and, independently, by Ebrahimi and Nasr-Isfahani, that every small n-abelian category is the n-cluster-tilting subcategory of an abelian category. In this talk we will focus on the relation between n-torsion classes in an n-abelian category MM and (classical) torsion classes of the abelian category AA in which MM is embedded. By considering functorially finite torsion classes, this will allow us to relate n-torsion classes with maximal tau_n-rigid objects in MM.Some of the results presented in this talk are part of a joint work by J. Asadollahi, P. Jørgensen, S. Schroll, H. Treffinger. The rest corresponds to an ongoing project by J. August, J. Haugland, K. Jacobsen, S. Kvamme,Y. Palu and H. Treffinger.

+ Yann PALU Torsion classes and tau-tilting in higher homological algebra, II 04/04/2022 14:30

Higher homological algebra was introduced by Iyama in the late 2000's. His point-of-view was that some classical results by Auslander and Auslander--Reiten were somehow 2-dimensional and should have n-dimensional equivalents. This new theory quickly attracted a lot of attention, with many authors generalising classical notions to the setting of higher homological algebra. Examples of such generalisations are the introduction of n-abelian categories by Jasso, n-angulated categories by Geiss--Keller--Oppermann, and n-torsion classes by Jørgensen.Recently, it was shown by Kvamme and, independently, by Ebrahimi and Nasr-Isfahani, that every small n-abelian category is the n-cluster-tilting subcategory of an abelian category. In this talk we will focus on the relation between n-torsion classes in an n-abelian category MM and (classical) torsion classes of the abelian category AA in which MM is embedded. By considering functorially finite torsion classes, this will allow us to relate n-torsion classes with maximal tau_n-rigid objects in MM.Some of the results presented in this talk are part of a joint work by J. Asadollahi, P. Jørgensen, S. Schroll, H. Treffinger. The rest corresponds to an ongoing project by J. August, J. Haugland, K. Jacobsen, S. Kvamme,Y. Palu and H. Treffinger.

+ Asilata Bapat Categorical q-deformed rational numbers via Bridgeland stability conditions 28/03/2022 14:00
We will discuss new categorical interpretations of two distinct q-deformations of the rational numbers. The first one, introduced by Morier-Genoud and Ovsienko in a different context, enjoys fascinating combinatorial, topological, and algebraic properties. The second one is a natural partner to the first, and is new. We obtain these deformations via boundary points of a compactification of the space of Bridgeland stability conditions on the 2-Calabi-Yau category of the A2 quiver. The talk is based on joint work with Louis Becker, Anand Deopurkar, and Anthony Licata.
+ Norihiro Hanihara Tilting theory via enhancements 21/03/2022 14:00
Tilting theory aims at giving equivalences among various triangulated categories, such as derived categories, cluster categories, and singularity categories. Constructing such an equivalence provides a mutual understanding of these categories. In this talk, we study tilting theory for singularity categories and cluster categories from the viewpoint of dg enhancements. We will first review their construction in terms of their enhancements, and then based on this we explain a general method of giving equivalences between singularity categories and cluster categories. Our main steps are existence of (weak) right Calabi-Yau structure on the dg singularity category of commutative Gorenstein rings, and a characterization of dg orbit categories among bigraded dg categories. This is a joint work with Osamu Iyama.
+ Jie Pan Positivity and polytope basis in cluster algebras via Newton polytopes 14/03/2022 14:00
We work in the generality of a totally sign-skew-symmetric (e.g. skew-symmetrizable) cluster algebra of rank $n$. We study the Newton polytopes of $F$-polynomials and, more generally, a family of polytopes $N_h$ indexed by vectors $h$ in $Z^n$. We use it to give a new proof of Laurent positivity and to construct what we call the polytope basis of the upper cluster algebra. The polytope basis consists of certain universally indecomposable Laurent polynomials. It is strongly positive and generalizes the greedy basis constructed by Lee-Li-Zelevinsky in rank 2. This is a report on joint work with Fang Li, cf. arXiv:2201.01440.
+ Alex TAKEDA The ribbon quiver complex and the noncommutative Legendre transform 07/03/2022 14:00
The structure of a fully extended oriented 2d TQFT is given by a Frobenius algebra. If one wants to lift this structure to a cohomological field theory, the correct notion is that of a Calabi-Yau algebra or category; the CohFT operations can be described by a certain graph complex. There are two different notions of Calabi-Yau structure on categories, both requiring some type of finiteness or dualizability. In this talk I will discuss a variation that works in non-dualizable cases as well; in this case the graphs get replaced by quivers. The resulting complex calculates the homology of certain moduli spaces of open-closed surfaces, and can be used to give a fully explicit description of these operations. In the second half of the talk, I will describe some of these constructions, including how to produce operations from smooth and/or relative Calabi-Yau structures, and explain how, in the smooth case, this can be thought of as a noncommutative version of the Legendre transform. This is joint work with M. Kontsevich and Y. Vlassopoulos.
+ Pierre-Guy PLAMONDON Cluster algebras, categorification, and some configuration spaces 28/02/2022 14:00
The real part of the configuration space M_{0,n} of n points on a projective line has a connected component which is closely related to the associahedron. As an affine variety, it is defined by explicit equations which are in close connection with exchange relations for cluster variables in type A. This has been generalized to all Dynkin types. In this talk, we will construct an affine variety associated to any representation-finite finite-dimensional algebra over an algebraically closed field. The equations defining the variety will be obtained from the F-polynomials of indecomposable modules over the algebra. This generalizes previous results, which can be recovered by applying our construction to Jacobian algebras in Dynkin types. This talk is based on an ongoing project with Nima Arkani-Hamed, Hadleigh Frost, Giulio Salvatori and Hugh Thomas.
+ Gonçalo TABUADA Jacques Tits motivic measure 21/02/2022 14:00
The Grothendieck ring of varieties, introduced in a letter from Alexander Grothendieck to Jean-Pierre Serre (August 16th 1964), plays an important role in algebraic geometry. However, despite the efforts of several mathematicians, the structure of this ring still remains poorly understood. In order to capture some of the flavor of Grothendieck’s ring of varieties, a few motivic measures have been built throughout the years. In this talk I will present a new motivic measure, called the Jacques Tits motivic measure, and describe some of its numerous applications.
+ Veronique Bazier-Matte Connection between knot theory and Jacobian algebras 14/02/2022 14:00
This is joint work with Ralf Schiffler. In knot theory, it is known that we can compute the Alexander polynomial of a knot from the lattice of Kauffman states of a knot diagram. Recently, my collaborator and I associated a quiver with a knot diagram. From this quiver, one can obtain a Jacobian algebra. It appears that the lattice of submodules of indecomposable modules over this algebra is in bijection with the lattice of Kauffman states. This bijection allows us to compute the Alexander polynomial of a knot with a specialization of the F-polynomial of any indecomposable module over this algebra. After a brief introduction to knot theory, I will explain how to compute an Alexander polynomial from a F-polynomial.
+ Nicolas WILLIAMS Equivalence of maximal green sequences 07/02/2022 14:00
It is natural to study the set of maximal green sequences of an algebra under an equivalence relation. The resulting set of equivalence classes has the structure of a poset; it is a lattice in type A, where the equivalence classes are in bijection with triangulations of three-dimensional cyclic polytopes. There are at least four appealing ways of defining an equivalence relation on maximal green sequences: commutation, exchange pairs, tau-rigid summands, and bricks. The main result of my talk will be that the first three methods define the same equivalence relation, while the fourth does not. This gives a surprising lack of duality between bricks, which correspond to simples, and tau-rigid summands, which correspond to projectives. This is a report on joint work in progress with Mikhail Gorsky.
+ Michael Wemyss Local Normal Forms of Noncommutative Functions 31/01/2022 14:00
This talk will explain how to generalise Arnold's results classifying commutative singularities into the noncommutative setting, and will classify finite dimensional Jacobi algebras arising on the d-loop quiver. The surprising thing is that a classification should exist at all, and it is even more surprising that ADE enters. I will spend most of my time explaining what the algebras are, why they classify, and how to intrinsically extract ADE information from them. At the end, I'll briefly explain why I'm really interested in this problem, the connection with different quivers, and the applications of the above classification to curve counting and birational geometry. This is all joint work with Gavin Brown.
+ Merlin CHRIST Gluing constructions of Ginzburg algebras and cluster categories 24/01/2022 14:00
Ginzburg algebras are a class of 3-CY dg algebras, which have attracted attention for their use in the categorification of cluster algebras. Given a marked surface with a triangulation, there is an associated Ginzburg algebra G. I will begin by describing how its derived category D^perf(G) can be glued from the derived categories of the relative Ginzburg algebras of the ideal triangles of the triangulation. We will see that the passage to Amiot's cluster category, defined as the quotient D^perf(G)/D^fin(G), does not commute with this gluing. As we will discuss, this can fixed by instead starting with the relative Ginzburg algebra of the triangulation and again applying Amiot's quotient formula. Remarkably, this resulting relative version of cluster category turns out to be equivalent to the 1-periodic topological Fukaya category of the surface.
+ Alfredo NÁJERA CHÁVEZ Deformation theory for finite cluster complexes 17/01/2022 14:00
Cluster complexes are a certain class of simplicial complexes that naturally arise in the theory of cluster algebras. They codify a wealth of fundamental information about cluster algebras. The purpose of this talk is to elaborate on a geometric relationship between cluster algebras and cluster complexes. In vague words, this relationship is the following: cluster algebras of finite cluster type with universal coefficients may be obtained via a torus action on a Hilbert scheme. In particular, we will discuss the deformation theory of the Stanley-Reisner ring associated to a finite cluster complex and present some applications related to the Gröbner theory of the ideal of relations among cluster and frozen variables of a cluster algebra of finite cluster type. Time permitting I will elaborate on how to generalize this approach to the context of tau-tilting finite algebras. This is based on a joint project with Nathan Ilten and Hipolito Treffinger whose first outcome is the preprint arXiv:2111.02566
+ Chris Brav Non-commutative string topology 10/01/2022 14:00
We explain how relative Calabi-Yau structures on dg functors, more generally relative orientations, give a non-commutative generalisation of oriented manifolds with boundary. We then construct genus zero string topology operations on the relative Hochschild homology HH_*(C,D) of a dg functor D —> C equipped with a relative orientation. More precisely, we prove a relative version of the cyclic Deligne conjecture, stating that this shifted relative Hochschild homology carries a natural structure of framed E_2-algebra. Examples include 1) the functor of induction of local systems for the inclusion of the boundary into an oriented manifold with boundary, in which case the relative Hochschild homology is identified with the relative loop homology 2) the functor of pushforward of coherent sheaves for the inclusion of the anti-canonical divisor into a variety, in which case relative Hochschild homology can be related to differential forms, and 3) various examples coming from representation theory.
+ Abel Lacabanne Higher rank Askey-Wilson algebras as skein algebras 13/12/2021 14:00
The skein algebra of a surface is built from the framed unoriented links in the thickened surface, modulo the Kauffman bracket relations. If the surface is the $4$-punctured sphere, it turns out that the skein algebra is a central extension of the universal Askey-Wilson algebra. De Bie, De Clercq and Van de Vijver proposed a definition of higher rank Askey-Wilson algebras, as a subalgebra of an $n$-fold tensor product of $U_q(\mathfrak{sl}_2)$. The aim of this talk is to explain an isomorphism between these higher rank Askey-Wilson algebras, and the skein algebras of punctured spheres. The diagrammatic flavour of the skein algebra provides then an efficient way to compute some relations between some elements of the Askey-Wilson algebra, notably the $q$-commutation relations discovered by De Clercq. This is joint work with J. Cooke.
+ Nicholas Ovenhouse q-Rational Numbers and Finite Schubert Varieties 06/12/2021 14:00
Recently, Morier-Genoud and Ovsienko generalized the notion of q-integers to include rational numbers. The q-analogue of a rational number is some rational function with integer coefficients. There are some known combinatorial interpretations of the numerators as rank generating functions of certain posets. I will review this interpretation, and re-phrase it in terms of lattice paths on "snake graphs". Using this snake graph interpretation, I will explain how the numerators count the number of points in some variety over a finite field. This variety is a union of Schubert cells in some Grassmannian.
+ Chris Fraser Automorphisms of open positroid varieties from braids 29/11/2021 14:00
Positroid varieties are distinguished subvarieties of Grassmannians which have cluster structure(s). I will give some reminders on the combinatorics underlying these cluster structures, partially based on a joint work with Melissa Sherman-Bennett. In a previous work, I described an action of a certain braid group on the top-dimensional positroid subvariety by "quasi" cluster automorphisms. I will explain how a similar statement can be extended to arbitrary open positroid varieties. This is joint with Bernhard Keller.
+ Kota Murakami Deformed Cartan matrices and generalized preprojective algebras, I 22/11/2021 14:00
In their study of deformed W-algebras associated with complex simple Lie algebras, E. Frenkel-Reshetikhin (1998) introduced certain two parameter deformations of the Cartan matrices. They play an important role in the representation theory of quantum affine algebras. In the former half of this talk, we explain a representation-theoretic interpretation of these deformed Cartan matrices and their inverses in terms of the generalized preprojective algebras recently introduced by Geiss-Leclerc-Schröer (2017). In the latter half of the talk, we discuss its application to the representation theory of quantum affine algebras in connection with the theory of cluster algebras.
+ Ryo Fujita Deformed Cartan matrices and generalized preprojective algebras, II 22/11/2021 14:30
In their study of deformed W-algebras associated with complex simple Lie algebras, E. Frenkel-Reshetikhin (1998) introduced certain two parameter deformations of the Cartan matrices. They play an important role in the representation theory of quantum affine algebras. In the former half of this talk, we explain a representation-theoretic interpretation of these deformed Cartan matrices and their inverses in terms of the generalized preprojective algebras recently introduced by Geiss-Leclerc-Schröer (2017). In the latter half of the talk, we discuss its application to the representation theory of quantum affine algebras in connection with the theory of cluster algebras.
+ Leonid Polterovich Lang Mou Generalized cluster dualities 15/11/2021 14:00
Fock and Goncharov introduced dualities between cluster varieties. I will explain how this duality under the framework of Gross-Hacking-Keel-Kontsevich can be naturally extended to generalized cluster varieties in the sense of Chekhov-Shapiro. In particular, I will construct generalized cluster scattering diagrams which are used to construct bases of functions on the dual varieties. As a generalized A-cluster variety yields a generalized cluster algebra, certain positivity property of the cluster monomials will be derived as a result of the positivity of the corresponding scattering diagram. This talk is mainly based on arXiv: 2110.02416.
+ Haicheng Zhang Hall algebras of extriangulated categories and quantum cluster algebras 08/11/2021 14:00
Firstly, we define the Hall algebra of an extriangulated category, a notion introduced by Nakaoka and Palu. Then for a finite acyclic valued quiver Q, we consider the Hall algebras of certain subcategories of the bounded derived category of the representation category of Q over a finite field, which are extriangulated categories. We recover the quantum Caldero-Chapoton formula via the Hall algebra approach and give the higher-dimensional (cluster) multiplication formulas in the quantum cluster algebra of Q with arbitrary coefficients, which can be viewed as the quantum version of the Caldero-Keller multiplication formula in the cluster algebra. This talk is based on the joint preprints arXiv:2005.10617, 2107.05883 and 2108.03558.
+ Lucien Hennecart (Canonical) bases of the elliptic Hall algebra 25/10/2021 14:00
The global nilpotent cone is a closed substack of the stack of Higgs sheaves on a smooth projective curve whose geometry has been studied in depth and is also an essential object in the geometric Langlands program. It is a highly singular stack and in particular it has several irreducible components which were rather recently explicitly described by Bozec. In this talk, we will concentrate on elliptic curves. We will recall Bozec's parametrization of the set of irreducible components of the global nilpotent cone and present another parametrization of the same set using (a refinement of) the Harder-Narasimhan stratification of the stack of coherent sheaves on the elliptic curve. Then, we raise the question of the comparison of these two bases, showing the emergence piecewise linear structures. We will also see how the second description can be useful to understand a part of the cohomological Hall algebra of an elliptic curve.
+ Matthew Pressland A cluster character for Y-variables 18/10/2021 14:00
+ Maxim Gurevich RSK-transform for L-parameters 11/10/2021 14:00
What is common between the Specht construction for modules over permutation groups, normal sequences of quiver Hecke algebra modules à la Kashiwara-Kim, and the local Langlands classification for GL_n ? I would like to show how these themes fit well together under a framework of a representation-theoretic Robinson-Schensted-Knuth transform, devised recently in my work with Erez Lapid on representations of p-adic groups. On one hand, RSK-standard modules are curious models for all smooth irreducible GL_n-representations. Yet, going through Bernstein-Rouquier categorical equivalences this notion is quantized into its natural existence in the realm of type A quiver Hecke algebras. A convenient bridge is thus portrayed between the cyclotomic approach of classifying simple modules through a generalized Specht construction, and the PBW-basis approach from Lusztig's work on quantum groups.
+ Giovanni CERULLI IRELLI On degeneration and extensions of symplectic and orthogonal quiver representations 04/10/2021 14:00
Motivated by linear degenerations of flag varieties, and the study of 2-nilpotent B-orbits for classical groups, I will review the representation theory of symmetric quivers, initiated by Derksen and Weyman in 2002. I will then focus on the problem of describing the orbit closures in this context and how to relate it to the orbit closures for the underlying quivers. In collaboration with M. Boos we have recently given an answer to this problem for symmetric quivers of finite type. I believe that this result is a very special case of a much deeper and general result that I will mention in the form of conjectures and open problems. The talk is based on the preprint version of my paper with Boos available on the arXiv as 2106.08666.
+ Ehud MEIR Interpolations of monoidal categories by invariant theory 05/07/2021 14:00
In this talk, I will present a recent construction that enables one to interpolate symmetric monoidal categories by interpolating algebraic structures and their automorphism groups. I will explain how one can recover the constructions of Deligne for categories such as Rep(S_t), Rep(O_t) and Rep(Sp_t), the constructions of Knop for wreath products with S_t and GL_t(O_r), where O_r is a finite quotient of a discrete valuation ring, and also the TQFT categories recently constructed from a rational function by Khovanov, Ostrik, and Kononov.
+ Mikhail Gorsky Braid varieties, positroids, and Legendrian links 28/06/2021 14:00
I will discuss a class of affine algebraic varieties associated with positive braids, their cluster structures and their relation to open Bott-Samelson varieties. First, I will explain our motivation which comes both from symplectic topology and from the study of HOMFLY-PT polynomials. Then we will discuss how the study of DG algebras associated with certain Legendrian links may help us to better understand the algebraic geometry of Richardson varieties in type A. I will illustrate our results and conjectures concerning this interplay between topology and algebraic geometry with the example of open positroid varieties in Grassmannians. If time permits, I will briefly explain conjectural relations between certain stratifications of braid varieties and cluster structures on their coordinate rings. This is joint work with Roger Casals, Eugene Gorsky, and José Simental.
+ Shunsuke KANO Categorical dynamical systems arising from sign-stable mutation loops 21/06/2021 14:00
A pair formed by a triangulated category and an autoequivalence is called a categorical dynamical system. Its complexity is measured by the so-called categorical entropy. In this talk, I will present a computation of the categorical entropies of categorical dynamical systems obtained by lifting a sign-stable mutation loop of a quiver to an autoequivalence of the derived category of the corresponding Ginzburg dg algebra. The notion of sign-stability is introduced as a generalization of the pseudo-Anosov property of mapping classes of surfaces. If time permits, we will discuss the pseudo-Anosovness of the autoequivalences constructed.
+ Justine FASQUEL Rationality at admissible levels of the simple W-algebras associated with subregular nilpotent elements in sp_4 14/06/2021 14:00
W-algebras are certain vertex algebras obtained from the quantized Drinfeld-Sokolov reduction of universal affine vertex algebras associated with a complex parameter k and a simple complex Lie algebra g. Their simple quotients are believed to be rational for specific values of k, called admissible, which depend on the choice of a nilpotent orbit in g. Here, by rationality, one means the complete reducibility of their positively graded modules. This conjecture was partially proved by Arakawa-van Ekeren and Creutzig-Linshaw. In this talk, I will discuss some consequences of the rationality for a very concrete example, namely the W-algebra associated with a subregular nilpotent element of the symplectic Lie algebra sp_4. In particular, we will be interested in certain actions on the W-algebra and the set of its simple modules.
+ Pierrick BOUSSEAU The flow tree formula for Donaldson-Thomas invariants of quivers with potentials 07/06/2021 14:00
Very generally, Donaldson-Thomas invariants are counts of stable objects in Calabi-Yau triangulated categories of dimension 3. A natural source of examples is provided by the representation theory of quivers with potentials. I will present a proof of a formula, conjectured by Alexandrov-Pioline from string-theory arguments, which computes Donaldson-Thomas invariants of a quiver with potential in terms of a much smaller set of "attractor invariants". The proof uses the framework of scattering diagrams to reorganize sequences of iterated applications of the Kontsevich-Soibelman wall-crossing formula. This is joint work with Hülya Argüz.
+ Damien CALAQUE Calabi-Yau structures for multiplicative preprojective algebras 31/05/2021 14:00
I will start by motivating and recalling Calabi-Yau structures and relative versions thereof. I will then provide several examples of Calabi-Yau structures occurring in the context of (dg-versions of) multiplicative preprojective algebras. The A_2 case, that we will describe in detail, will be used as a building block for general quivers. At the end of the talk, I will describe a strategy for a comparison with other constructions, for instance Van den Bergh's quasi-bi-hamiltonian structures. This is a report on joint work with Tristan Bozec and Sarah Scherotzke.
+ Dan KAPLAN Multiplicative preprojective algebras for Dynkin quivers 24/05/2021 14:00
Crawley-Boevey and Shaw defined the multiplicative preprojective algebra to understand Kac’s middle convolution and to solve the Deligne-Simpson problem. In Shaw’s thesis he noticed a curious phenomenon: for the D_4 quiver the multiplicative preprojective algebra (with parameter q=1) is isomorphic to the (additive) preprojective algebra if and only if the underlying field has characteristic not two. Later, Crawley-Boevey proved the multiplicative and additive preprojective algebras are isomorphic for all Dynkin quivers over the complex numbers. Recent work of Etgü-Lekili and Lekili-Ueda, in the dg-setting, sharpens the result to hold over fields of good characteristic, meaning characteristic not 2 in type D, not 2 or 3 in type E and not 2, 3, or 5 for E_8. Neither work produces an isomorphism. In this talk, I will explain how to construct these isomorphisms and prove their non-existence in the bad (i.e., not good) characteristics. For each bad characteristic, a single class in zeroth Hochschild homology obstructs the existence of an isomorphism. Time permitting, I’ll explain how to interpret these results in the dg-setting where the 2-Calabi-Yau property allows us to recast these obstructions as non-trivial deformations, using Van den Bergh duality.
+ Sachin GAUTAM Poles of finite-dimensional representations of Yangians 17/05/2021 14:00
The Yangian associated to a simple Lie algebra g is a Hopf algebra which quantizes the Lie algebra of polynomials g[t]. Its finite-dimensional representation theory has remarkable connections with equivariant cohomology, combinatorics, integrable systems and mathematical physics. Concretely, a finite-dimensional representation of the Yangian is prescribed by a finite collection of operators whose coefficients are rational functions, satisfying a list of commutation relations. In this talk I will give an explicit combinatorial description of the sets of poles of the rational currents of the Yangian, acting on an irreducible finite-dimensional representation. This result uses the generalization of Baxter's Q-operators obtained by Frenkel-Hernandez. Based on a joint work with Curtis Wendlandt (arxiv:2009.06427).
+ Pierre BAUMANN Explicit calculations in the geometric Satake equivalence 10/05/2021 14:00
Let $G$ be a complex connected reductive group. As shown by Mirković and Vilonen, the geometric Satake equivalence yields a basis in each irreducible rational representation of $G$, defined out of algebraic cycles in the affine Grassmannian of the Langlands dual of $G$. Goncharov and Shen extended this construction to each tensor product of irreducible representations. We will investigate the properties of all these bases and explain a method to compute them. Based on a joint work with Peter Littelmann and Stéphane Gaussent.
+ Alexander TSYMBALIUK Quantum loop groups and shuffle algebras via Lyndon words 03/05/2021 14:00
Classical q-shuffle algebras provide combinatorial models for the positive half U_q(n) of a finite quantum group. We define a loop version of this construction, yielding a combinatorial model for the positive half U_q(Ln) of a quantum loop group. In particular, we construct a PBW basis of U_q(Ln) indexed by standard Lyndon words, generalizing the work of Lalonde-Ram, Leclerc and Rosso in the U_q(n) case. We also connect this to Enriquez' degeneration A of the elliptic algebras of Feigin-Odesskii, proving a conjecture that describes the image of the embedding U_q(Ln) ---> A in terms of pole and wheel conditions. Joint work with Andrei Negut.
+ Gregg MUSIKER Combinatorial Expansion Formulas for Decorated Super-Teichmüller Spaces 26/04/2021 14:00
Motivated by the definition of super Teichmuller spaces, and Penner-Zeitlin's recent extension of this definition to decorated super Teichmuller space, as examples of super Riemann surfaces, we use the super Ptolemy relations to obtain formulas for super lambda-lengths associated to arcs in a bordered surface. In the special case of a disk, we are able to give combinatorial expansion formulas for the super lambda-lengths associated to diagonals of a polygon in the spirit of Ralf Schiffler's T-path formulas for type A cluster algebras. We further connect our formulas to the super-friezes of Morier-Genoud, Ovsienko, and Tabachnikov, and obtain partial progress towards defining super cluster algebras of type A. In particular, following Penner-Zeitlin, we are able to get formulas (up to signs) for the mu-invariants associated to triangles in a triangulated polygon, and explain how these provide a step towards understanding odd variables of a super cluster algebra. This is joint work with Nicholas Ovenhouse and Sylvester Zhang.
+ Nicholas WILLIAMS The higher Stasheff–Tamari orders in representation theory 19/04/2021 14:00
Oppermann and Thomas show that tilting modules over Iyama's higher Auslander algebras of type A are in bijection with triangulations of even-dimensional cyclic polytopes. Triangulations of cyclic polytopes are partially ordered in two natural ways known as the higher Stasheff–Tamari orders, which were introduced in the 1990s by Kapranov, Voevodsky, Edelman, and Reiner as higher-dimensional generalisations of the Tamari lattice. These two partial orders were conjectured to be equal in 1996 by Edelman and Reiner, but this is still an open problem. We show how the higher Stasheff–Tamari orders correspond in even dimensions to natural orders on tilting modules which were studied by Riedtmann, Schofield, Happel, and Unger. This then allows us to complete the picture of Oppermann and Thomas by showing that triangulations of odd-dimensional cyclic polytopes correspond to equivalence classes of d-maximal green sequences, which we introduce as higher-dimensional analogues of Keller’s maximal green sequences. We show that the higher Stasheff–Tamari orders correspond to natural orders on equivalence classes of d-maximal green sequences, which relate to the no-gap conjecture of Brüstle, Dupont, and Perotin. If time permits, we will also briefly discuss more recent work concerning the relation between the first higher Stasheff–Tamari orders and the higher Bruhat orders, which are higher-dimensional analogues of the weak Bruhat order on the symmetric group.
+ Erik DARPOE Periodic trivial extension algebras and fractionally Calabi–Yau algebras 12/04/2021 14:00
An important open problem in the homological algebra of self-injective algebras is to characterise periodic algebras. An algebra B is said to be periodic if if has a periodic projective resolution as a B-B-bimodule. In this talk, I will present a solution to this problem for trivial extension algebras: the trivial extension algebra T(A) of a finite-dimensional algebra A is periodic if and only if A has finite global dimension and is fractionally Calabi-Yau. This is based on joint work with Chan, Iyama and Marczinzik.
+ Sergey MOZGOVOY Operadic approach to wall-crossing and attractor invariants 29/03/2021 14:00
Wall-crossing describes how various invariants in algebraic geometry and theoretical physics transform under the variation of parameters. In this talk I will discuss a framework, reminiscent of collections and plethysms in the theory of operads, that concenptualizes those transformation rules. I will describe how some new and existing wall-crossing formulas can be proved using this approach. In particular, I will discuss applications to attractor invariants (also called initial data in the theory of scattering diagrams).
+ Alexander VESELOV Automorphic Lie algebras and modular forms 22/03/2021 14:00
The automorphic Lie algebras can be viewed as generalisations of twisted loop Lie algebras, when a group G acts holomorphically and discretely on a Riemann surface and by automorphisms on the chosen Lie algebra. In the talk we will discuss the automorphic Lie algebras of modular type, when G is a finite index subgroup of the modular group SL(2,Z)$ acting on the upper half plane. In the case when the action of G can be extended to SL(2,C) we prove analogues of Kac’s isomorphism theorem for the twisted loop Lie algebras. For the modular group and some of its principal congruence subgroups we provide an explicit description of such isomorphisms using the classical theory of modular forms. The talk is based on the ongoing joint work with Vincent Knibbeler and Sara Lombardo.
+ Deniz KUS Prime representations in the HL category 15/03/2021 14:00
Generators and relations of graded limits of certain finite dimensional irreducible representations of quantum affine algebras have been determined in recent years. For example, the representations in the Hernandez-Leclerc category corresponding to cluster variables appear to be certain truncations of representations for current algebras and tensor products are related to the notion of fusion products. In this talk we will discuss some known results on this topic and study the classical and graded characters of prime representations in the HL category.
+ Ryo FUJITA Isomorphims among quantum Grothendieck rings and propagation of positivity 08/03/2021 14:00
For a complex simple Lie algebra $\mathfrak{g}$, finite-dimensional representations of its quantum loop algebra form an interesting monoidal abelian category, which has been studied from various perspectives. Related to the fundamental problem of determining the characters of irreducible representations, we consider its quantum Grothendieck ring, a 1-parameter deformation of the usual Grothendieck ring. When $\mathfrak{g}$ is of simply-laced type, Nakajima and Varagnolo-Vasserot proved that it enjoys some positivity properties based on the geometry of quiver varieties. In this talk, we show that the same positivities hold also for non-simply-laced type by establishing an isomorphism between the quantum Grothendieck ring of non-simply-laced type and that of ''unfolded'' simply-laced type. In addition, we find that an analog of Kazhdan-Lusztig conjecture holds for several new cases in non-simply-laced type. This is a joint work with David Hernandez, Se-jin Oh, and Hironori Oya.
+ Amnon YEKUTIELI Rigidity, Residues and Duality: Overview and Recent Progress 01/03/2021 14:00
Let K be a regular noetherian ring. I will begin by explaining what is a rigid dualizing complex over an essentially finite type (EFT) K-ring A. This concept was introduced by Van den Bergh in the 1990's, in the setting of noncommutative algebra. It was imported to commutative algebra by Zhang and myself around 2005, where it was made functorial, and it was also expanded to the arithmetic setting (no base field). The arithmetic setting required the use of DG ring resolutions, and in this aspect there were some major errors in our early treatment. These errors have recently been corrected, in joint work with Ornaghi and Singh. Moreover, we have established the forward functoriality of rigid dualizing complexes w.r.t essentially etale ring homomorphisms, and their backward functoriality w.r.t. finite ring homomorphisms. These results mean that we have a twisted induction pseudofunctor, constructed in a totally algebraic way (rings only, no geometry). Looking to the future, we plan to study a more refined notion: rigid residue complexes. These are complexes of quasi-coherent sheaves in the big etale site of EFT K-rings, and they admit backward functoriality, called ind-rigid traces, w.r.t. arbitrary ring homomorphisms. Rigid residue complexes can be easily glued on EFT K-schemes, and they still have the ind-rigid traces w.r.t. arbitrary scheme maps. The twisted induction now becomes the geometric twisted inverse image pseudofunctor $f \mapsto f^!$. We expect to prove the Rigid Residue Theorem and the Rigid Duality Theorem for proper maps of EFT K-schemes, thus recovering almost all of the theory in the original book “Residues and Duality”, in a very explicit way. The etale functoriality implies that every finite type Deligne-Mumford (DM) K‑stack admits a rigid residue complex. Here too we have the $f \mapsto f^!$ pseudofunctor. For a map of DM stacks there is the ind-rigid trace. Under a mild technical condition, we expect to prove the Rigid Residue Theorem for proper maps of DM stacks, and the Rigid Duality Theorem for such maps that are also tame. More details are available in the eprint with the same title at arxiv.org/abs/2102.00255
+ Valentin OVSIENKO Combinatorial and analytic properties of q-deformed real numbers 22/02/2021 14:00
I will explain a recent notion of q-deformed real numbers, and discuss its various combinatorial and analytic properties. A " q-deformed real" is a Laurent series in one variable, q, with integer coefficients. The subject is connected to different theories, such as knot invariants, continued fractions, and cluster algebras. I will formulate a challenging conjecture about the convergence of the series arising as q-deformed real numbers. (Here we understand q as a complex variable.) The conjecture is proved in particular cases and concrete examples. In the most simple examples of q-Fibonacci and q-Pell numbers, the explicit formulas for the radius of convergence are very similar to certain formulas of Ramanujan. The talk is based on a joint work with Ludivine Leclere, Sophie Morier-Genoud and Alexander Veselov.
+ Milen YAKIMOV Root of unity quantum cluster algebras 15/02/2021 14:00
We will describe a theory of root of unity quantum cluster algebras, which are not necessarily specializations of quantum cluster algebras. All such algebras are shown to be polynomial identity (PI) algebras. Inside each of them, we construct a canonical central subalgebra which is proved to be isomorphic to the underlying cluster algebra. (In turn, this is used to show that two exchange graphs are canonically isomorphic). This setting generalizes the De Concini-Kac-Procesi central subalgebras in big quantum groups and presents a general framework for studying the representation theory of quantum algebras at roots of unity by means of cluster algebras as the relevant data becomes (PI algebra, canonical central subalgebra)=(root of unity quantum cluster algebra, underlying cluster algebra). We also obtain a formula for the corresponding discriminant in this general setting that can be applied in many concrete situations of interest, such as the discriminants of all root of unity quantum unipotent cells for symmetrizable Kac-Moody algebras, defined integrally over Z[root of unity]. This is a joint work with Bach Nguyen (Xavier Univ) and Kurt Trampel (Notre Dame Univ).
+ Sondre KVAMME Admissibly finitely presented functors for exact categories 08/02/2021 14:00
In this talk we introduce the category of admissibly finitely presented functors mod_{adm}(E) for an exact category E. In particular, we characterize exact categories of the form mod_{adm}(E), and show that they have properties similar to module categories of Auslander algebras. For a fixed idempotent complete category C, we also use this construction to show that exact structures on C correspond to certain resolving subcategories in mod(C). This is joint work with Ruben Henrard and Adam-Christiaan van Roosmalen.
+ Pedro TAMAROFF Poincaré--Birkhoff--Witt theorems: homotopical and effective computational methods for universal envelopes 01/02/2021 14:00
In joint work with V. Dotsenko, we developed a categorical framework for Poincaré-Birkhoff-Witt type theorems about universal enveloping algebras of various algebraic structures, and used methods of term rewriting for operads to obtain new PBW theorems, in particular answering an open question of J.-L. Loday. Later, in joint work with A. Khoroshkin, we developed a formalism to study Poincaré–Birkhoff–Witt type theorems for universal envelopes of algebras over differential graded operads, motivated by the problem of computing the universal enveloping algebra functor on dg Lie algebras in the homotopy category. Our formalism allows us, among other things, to obtain a homotopy invariant version of the classical Poincaré–Birkhoff–Witt theorem for universal envelopes of Lie algebras, and extend Quillen's quasi-isomorphism C(g) ---> BU(g) to homotopy Lie algebras. I will survey and explain the role homological algebra, homotopical algebra, and effective computational methods play in the main results obtained with both V. Dotsenko (1804.06485) and A. Khoroshikin (2003.06055) and, if time allows, explain a new direction in which these methods can be used to study certain operads as universal envelopes of pre-Lie algebras.
+ Victoria LEBED Homotopical tools for computing rack homology 25/01/2021 14:00
Racks are certain algebraic structures yielding powerful tools for knot theory, Hopf algebra classification and other areas. Rack homology plays a crucial role in these applications. The homology of a rack is very easy to define (via an explicit chain complex), but extremely difficult to compute. Until recently, the full homology was known only for three families of racks. Together with Markus Szymik, we added a forth family to this list, the family of permutation racks. More importantly, our work unexpectedly brought homotopical methods into the area, and showed that in spite of their abstract flavour they can yield concrete computations. The necessary background on racks and their homology, as well as an overview of the tools previously used for its computation, will be given.
+ Estanislao HERSCOVICH Double quasi-Poisson algebras are pre-Calabi-Yau 18/01/2021 14:00
Double Poisson and double quasi-Poisson algebras were introduced by M. Van den Bergh in his study of noncommutative quasi-Poisson geometry. Namely, they satisfy the so-called Kontsevich-Rosenberg principle, since the representation scheme of a double (quasi-)Poisson algebra has a natural (quasi-)Poisson structure. On the other hand, N. Iyudu and M. Kontsevich found a link between double Poisson algebras and pre-Calabi-Yau algebras, a notion introduced by Kontsevich and Y. Vlassopoulos. The aim of this talk will be to explain how such a connection can be extended to double quasi-Poisson algebras, which thus give rise to pre-Calabi-Yau algebras. This pre-Calabi-Yau structure is however more involved in the case of double quasi-Poisson algebras since, in particular, we get an infinite number of nonvanishing higher multiplications for the associated pre-Calabi-Yau algebra, which involve the Bernoulli numbers.
+ Manon Defosseux Brownian motion in the unit interval and the Littelmann path model 11/01/2021 14:00
We will present for a Brownian motion in the unit interval a Pitman type theorem obtained recently in joint work with Philippe Bougerol. We will focus on algebraic aspects and will explain how it is related to the Littelmann path model for an affine Kac–Moody algebra of extended type $A_1$.
+ Emmanuel LETELLIER E-series of character varieties associated with non orientable surfaces 14/12/2020 14:00
In this talk we will be interested in two kinds of character varieties associated to a compact non-orientable surface S. The first one is just the quotient stack of all representations of the fundamental group of S in GL(n,C). For the second one, we consider k punctures of S as well as k semisimple conjugacy classes of GL(n,C). We then consider the stack of anti-invariant local systems on the orientation covering of S with local monodromies around the punctures in the prescribed conjugacy classes. We compute the number of points of these spaces over finite fields and we give a cohomological interpretation of our counting formulas. For the second kind of character varieties, we give a conjectural formula for the mixed Poincaré series in terms of Macdonald symmetric functions.
+ Ruslan MAKSIMAU KLR algebras for curves and semi-cuspidal representations 07/12/2020 14:00
+ Markus REINEKE Wild quantum dilogarithm identities 30/11/2020 14:00
+ Sarah Scherotzke Cotangent complexes of moduli spaces and Ginzburg dg algebras 23/11/2020 14:00
We start by giving an introduction to the notion of moduli stack of a dg category. Then we will explain what shifted symplectic structures are and how they are connected to Calabi-Yau structures on dg categories. More concretely, we will show that the cotangent complex of the moduli stack of a dg category A is isomorphic to the moduli stack of the *Calabi-Yau completion* of A. This answers a conjecture of Keller-Yeung. This is joint work with Damien Calaque and Tristan Bozec arXiv:2006.01069.
+ Eleonore Faber McKay quivers of complex reflection groups and the McKay correspondence 16/11/2020 14:00
Finite complex reflection groups were classified by Shepherd and Todd: up to finitely many exceptions they are the groups G(r,p,n). In this talk we give a combinatorial description of the McKay quivers of these groups. Further we will comment on a McKay correspondence for complex reflection groups. This is joint work with R.-O. Buchweitz, C. Ingalls, and M. Lewis.
+ Stéphane Launois Catenarity and Tauvel’s height formula for quantum nilpotent algebras 09/11/2020 14:00
This talk is based on joint work with Ken Goodearl and Tom Lenagan. I will explain why quantum nilpotent algebras are catenary, that is, why all saturated chains of inclusions of prime ideals in a quantum nilpotent algebra have the same length. As a corollary, we obtain that Tauvel’s height formula holds for quantum nilpotent algebras. Time permitting, I will present a different strategy to prove the latter result.
+ Elie CASBI Equivariant multiplicities of simply-laced type flag minors 02/11/2020 14:00
The study of remarkable bases of (quantum) coordinate rings has been an area of intensive research since the early 90's. For instance, the multiplicative properties of these bases (in particular the dual canonical basis) was one of the main motivations for the introduction of cluster algebras by Fomin and Zelevinsky around 2000. In recent work, Baumann-Kamnitzer-Knutson introduced an algebra morphism  $\overline{D}$ from the coordinate algebra $\mathbb{C}[N]$ of a maximal unipotent subgroup $N$ to the function field of a maximal torus. It is related to the geometry of Mirkovic-Vilonen cycles via the notion of equivariant multiplicity. This morphism turns out to be useful for comparing good bases of the coordinate algebra $\mathbb{C}[N]$. We will focus on comparing the values taken by $\overline{D}$ on several distinguished elements of the Mirkovic-Vilonen basis and the dual canonical basis. For the latter one, we will use Kang-Kashiwara-Kim-Oh's monoidal categorification of the cluster structure of the cluster structure of $\mathbb{C}[N]$ via quiver Hecke algebras as well as recent results by Kashiwara-Kim. This will lead us to an explicit description of the images under $\overline{D}$ of the flag minors of $\mathbb{C}[N]$ as well as remarkable identities between them.
+ Wai-kit Yeung Pre-Calabi-Yau algebras 26/10/2020 14:00
Pre-Calabi-Yau categories are algebraic structures first studied by Kontsevich and Vlassopoulos. They can be viewed as a noncommutative analogue of Poisson structures, just like Calabi-Yau structures can be viewed as a noncommutative analogue of symplectic structures. In this talk, we discuss several aspects of this notion.
+ Norihiro Hanihara Cluster categories of formal dg algebras 19/10/2020 14:00
Cluster categories are Calabi-Yau triangulated categories endowed with cluster tilting objects. They have played an important role in the (additive) categorification of cluster algebras. We study the version developed by Amiot-Guo-Keller, which is defined in terms of CY dg algebras. Given a negatively graded (non-dg) CY algebra, we view it as a dg algebra with trivial differential. We give a description of the cluster category of such a formal dg algebra as the triangulated hull of an orbit category of a derived category, and also as the singularity category of a finite dimensional algebra. Furthermore, if time permits, we will talk about a certain converse of this construction, giving a Morita-type theorem for CY triangulated categories arising from hereditary algebras, partially generalizing that of Keller-Reiten.
+ Ryo FUJITA Twisted Auslander-Reiten quivers, quantum Cartan matrix and representation theory of quantum affine algebras 12/10/2020 14:00
For a complex simple Lie algebra $g$, its quantum Cartan matrix plays an important role in the representation theory of the quantum affine algebra of $g$. When $g$ is of type ADE, Hernandez-Leclerc (2015) related its quantum Cartan matrix with the representation theory of Dynkin quivers and hence with the combinatorics of adapted words in the Weyl group of the corresponding ADE type. In this talk, we introduce the notion of Q-data, which can be regarded as a combinatorial generalization of a Dynkin quiver with height function, and its twisted Auslander-Reiten quiver. Using them, we relate the quantum Cartan matrix of type BCFG with the combinatorics of twisted adapted words in the Weyl group of the corresponding unfolded ADE type introduced by Oh-Suh (2019). Also, we see their relation to the representation theory of quantum affine algebras. For example, we present a (partially conjectural) unified expression of the denominators of R-matrices between the Kirillov-Reshetikhin modules in terms of the quantum Cartan matrices. This is a joint work with Se-jin Oh.
+ Dylan ALLEGRETTI Wall-crossing and differential equations 05/10/2020 14:00
The Kontsevich-Soibelman wall-crossing formula describes the wall-crossing behavior of BPS invariants in Donaldson-Thomas theory. It can be formulated as an identity between (possibly infinite) products of automorphisms of a formal power series ring. In this talk, I will explain how these same products also appear in the exact WKB analysis of Schrödinger's equation. In this context, they describe the Stokes phenomenon for objects known as Voros symbols.
+ Zhengfang WANG $B_\infty$-algebras and Keller’s conjecture for singular Hochschild cohomology 28/09/2020 14:00
+ Maria Julia Redondo $L_\infty$-structure on Barzdell's complex for monomial algebras 21/09/2020 14:00
When dealing with a monomial algebra $A$, Bardzell’s complex $B(A)$ has shown to be more efficient for computing Hochschild cohomology groups of $A$ than the Hochschild complex $C(A)$. Since $C(A)[1]$ is a dg Lie algebra, it is natural to ask if the comparison morphisms between these complexes allows us to transfer the dg Lie structure to $B(A)[1]$. This is true for radical square zero algebras, but it is not true in general for monomial algebras. In this talk, I will describe an explicit $L_\infty$-structure on $B(A)$ that induces a weak equivalence of $L_\infty$-algebras between $B(A)$ and $C(A)$. This allows us to describe the Maurer-Cartan equation in terms of elements of degree 2 in $B(A)$ and make concrete computations when $A$ is a truncated monomial algebra.
+ Liran Shaul The Cohen–Macaulay property in derived algebraic geometry 14/09/2020 14:00
+ Osamu IYAMA Tilting theory of contracted preprojective algebras and cDV singularities 13/07/2020 14:00

A preprojective algebra of non-Dynkin type has a family of tilting modules associated with the elements in the corresponding Coxeter group W. This family is useful to study the representation theory of the preprojective algebra and also to categorify cluster algebras.
In this talk, I will discuss tilting theory of a contracted preprojective algebra, which is a subalgebra eAe of a preprojective algebra A given by an idempotent e of A. It has a family of tilting modules associated with the chambers in the contracted Tits cone. They correspond bijectively with certain double cosets in W modulo parabolic subgroups. 
I will apply these results to classify a certain family of reflexive modules over a cDV singularities R, called maximal modifying (=MM) modules. We construct an injective map from MM R-modules to tilting modules over a contracted preprojective algebra of extended Dynkin type. This is bijective if R has at worst an isolated singularity. We can recover previous results (Burban-I-Keller-Reiten, I-Wemyss) as a very special case.
This is joint work with Michael Wemyss.

+ Xin FANG (房欣) Exact structures and degenerations of Hall algebras, I 06/07/2020 14:00

In this talk, we will explain relations between exact structures on an additively finite additive category and degenerations of the associated Hall algebras. The first part of the talk will be devoted to the main motivation provided by concrete examples of degenerations of negative parts of quantum groups arising as Hall algebras of quiver representations. We will then turn to Lie theory in order to establish a link from these examples to tropical flag varieties and certain quiver Grassmannians. In the second part of the talk we will present results in the general case and sketch their proofs based on Auslander-Reiten theory. If time permits, we will briefly discuss further conjectural examples and generalizations.

+ Mikhail Gorsky Exact structures and degenerations of Hall algebras, II 06/07/2020 14:30

In this talk, we will explain relations between exact structures on an additively finite additive category and degenerations of the associated Hall algebras. The first part of the talk will be devoted to the main motivation provided by concrete examples of degenerations of negative parts of quantum groups arising as Hall algebras of quiver representations. We will then turn to Lie theory in order to establish a link from these examples to tropical flag varieties and certain quiver Grassmannians. In the second part of the talk we will present results in the general case and sketch their proofs based on Auslander-Reiten theory. If time permits, we will briefly discuss further conjectural examples and generalizations.

+ Linyuan Liu (刘琳媛) Modular Brylinski-Kostant filtration of tilting modules 29/06/2020 14:00

Let $G$ be a reductive algebraic group over a field $k$. When $k=\mathbb{C}$, R. K. Brylinski constructed a filtration of weight spaces of a $G$-module, using the action of a principal nilpotent element of the Lie algebra, and proved that this filtration corresponds to Lusztig's $q$-analogue of the weight multiplicity. Later, Ginzburg discovered that this filtration has an interesting geometric interpretation via the geometric Satake correspondence. Recently, we managed to generalise this result to the case where $k$ is a field of good positive characteristics. I will give a brief introduction to both historical results and our new result in the talk.

+ Myungho Kim Braid group action on the module category of quantum affine algebras 22/06/2020 14:00

Let $g_0$ be a simple Lie algebra of type $ADE$ and let $U′_q(g)$ be the corresponding untwisted quantum affine algebra. We found an action of the braid group $B(g_0)$ on the quantum Grothendieck ring $K_t(g)$ of Hernandez-Leclerc's category $C^0_g$. In the case of $g_0=A_{N−1}$, we construct a monoidal autofunctor $S_i$ for each integer $i$ on a category $T_N$ arising from the  quiver Hecke algebra of type $A_\infty$. 
Since there is an isomorphism between the Grothendieck ring $K(T_N)$ of $T_N$ and the quantum Grothendieck ring $K_t(A^(1)_{N−1})$, the functors $S_i$, $(i=1, ..., N-1)$, recover the action of the braid group $B(A_{N−1})$. 
This is a joint work with Masaki Kashiwara, Euiyong Park and Se-jin Oh.

+ Christof GEISS Generic bases for surface cluster algebras 15/06/2020 14:00

This is a report on joint work with D. Labardini-Fragoso and J. Schröer. We show that for most marked surfaces with non-empty boundary, possibly with punctures, the generic Caldero-Chapoton functions form a basis of the corresponding cluster algebras for any choice of geometric coefficients. For surfaces without punctures the $\tau$-reduced components of the corresponding gentle Jacobian algebra are naturally parametrized by X-laminations of the surface, and it is easy to see that for principal coefficients, the generic basis coincides with the bangle basis introduced by Musiker-Schiffler-Williams.

+ Baptiste ROGNERUD Combinatorics of quasi-hereditary structures, I 08/06/2020 14:00

Quasi-hereditary algebras were introduced by Cline, Parshall and Scott as a tool to study highest weight theories which arise in the representation theories of semi-simple complex Lie algebras and reductive groups. Surprisingly, there are now many examples of such algebras, such as Schur algebras, algebras of global dimension at most two, incidence algebras and many more. 

A quasi-hereditary algebra is an Artin algebra together with a partial order on its set of isomorphism classes of simple modules which satisfies certain conditions. In the early examples the partial order predated (and motivated) the theory, so the choice was clear. However, there are instances of quasi-hereditary algebras where there is no natural choice for the partial ordering and even if there is such a natural choice, one may wonder about all the possible orderings.

In this talk we will explain that all these choices for an algebra $A$ can be organized in a finite partial order which is in relation with the tilting theory of $A$. In a second part of the talk we will focus on the case where $A$ is the path algebra of a Dynkin quiver.

+ Yuta Kimura Combinatorics of quasi-hereditary structures, II 08/06/2020 14:30

Quasi-hereditary algebras were introduced by Cline, Parshall and Scott as a tool to study highest weight theories which arise in the representation theories of semi-simple complex Lie algebras and reductive groups. Surprisingly, there are now many examples of such algebras, such as Schur algebras, algebras of global dimension at most two, incidence algebras and many more. 

A quasi-hereditary algebra is an Artin algebra together with a partial order on its set of isomorphism classes of simple modules which satisfies certain conditions. In the early examples the partial order predated (and motivated) the theory, so the choice was clear. However, there are instances of quasi-hereditary algebras where there is no natural choice for the partial ordering and even if there is such a natural choice, one may wonder about all the possible orderings.

In this talk we will explain that all these choices for an algebra $A$ can be organized in a finite partial order which is in relation with the tilting theory of $A$. In a second part of the talk we will focus on the case where $A$ is the path algebra of a Dynkin quiver.

+ Gustavo JASSO The symplectic geometry of higher Auslander algebras 01/06/2020 14:00

It is well known that the partially wrapped Fukaya category of a marked
disk is equivalent to the perfect derived category of a Dynkin quiver of
type A. In this talk I will present a higher-dimensional generalisation
of this equivalence which reveals a connection between three a
priori unrelated subjects:

* Floer theory of symmetric products of marked surfaces
* Higher Auslander-Reiten theory in the sense of Iyama
* Waldhausen K-theory of differential graded categories

If time permits, as a first application of the above relationship, I
will outline a symplecto-geometric proof of a recent result of Beckert
concerning the derived equivalence between higher Auslander algebras of
different dimensions. This is a report on joint work with Tobias
Dyckerhoff and Yankı Lekili.

+ Hironori OYA Newton-Okounkov polytopes of Schubert varieties arising from cluster structures and representation-theoretic polytopes 25/05/2020 14:00
The theory of Newton-Okounkov bodies is a generalization of 
that of Newton polytopes for toric varieties. One of the ingredients for 
the definition of a Newton-Okounkov body is a valuation on the function 
field of a given projective variety. In this talk, we consider Newton-
Okounkov bodies of Schubert varieties defined from specific valuations 
which generalize extended g-vectors in cluster theory. We show that they 
provide polytopes unimodularly equivalent to string polytopes and 
Nakashima-Zelevinsky polytopes, both of which are well-known polytopes 
in representation theory. Indeed, this framework allows us to connect 
string polytopes with Nakashima-Zelevinsky polytopes by tropicalized 
cluster mutations. 
This talk is based on a joint work with Naoki Fujita.
+ Fan QIN Dual canonical bases and quantum cluster algebras 18/05/2020 14:00

Fomin and Zelevinsky invented cluster algebras, which are algebras with distinguished generators called cluster variables. For any symmetrizable Kac-Moody algebra and Weyl group element, the corresponding quantum unipotent subgroup possesses the dual canonical basis, and it can be viewed as a (quantum) cluster algebra. As a main motivation by Fomin and Zelevinsky, it has been long conjectured that the quantum cluster monomials (certain monomials of cluster variables) belong to the dual canonical basis up to scalar multiples. We sketch a proof of this conjecture in full generality.

+ Adrien BROCHIER On invertible braided tensor categories 11/05/2020 14:00

Dualizability and invertibility are two natural properties one can ask for objects in (possibly
higher) symmetric monoidal categories. On the one hand, it recovers as special cases various
important notions in geometry and representation theory. On the other hand, it connects those
notions to topology via the cobordism hypothesis. I will explain various examples of this philosophy, with an emphasis on applications to finite braided tensor categories. This is based on joint work with D. Jordan, P. Safronov and N. Snyder. 

+ Michael CUNTZ Frieze patterns with coefficients 04/05/2020 14:00

Friezes with coefficients are maps assigning numbers to the edges and diagonals of a regular polygon such that all Ptolemy relations for crossing diagonals are satisfied. These are relevant for example for the study of cluster algebras, in a special case they may also be viewed as root systems of certain quantum groups. 
In this talk I will report on recent results on subpolygons of friezes. Depending on the domain of the entries of the friezes, these subpolygons satisfy interesting arithmetic obstructions.

+ Pierre-Guy PLAMONDON Associahedra and the Grothendieck group of an extriangulated structure on the cluster category 27/04/2020 14:00

The associahedron is a polytope that encodes Catalan families. One of its many avatars is as a polytopal realization of the g-vector fan of a cluster algebra of type A.  Given a cluster algebra with fixed initial seed, the space of all polytopal realizations of its g-vector fan has been of interest to physicists, appearing for instance in the work of Arkani-Hamed, Bai, He and Yan. 

In this talk, we will see how a description of the set of all polytopal realizations of the g-vector fan of any cluster algebra of finite type with any initial seed can be described by looking for a minimal set of relations between its g-vectors.  To find such a set, we will see how a sub-extriangulated structure of the triangulated structure of the cluster category allows for a categorification of g-vectors, and find all relations in its Grothendieck group. 

This is a report on a joint work with Arnau Padrol, Yann Palu and Vincent Pilaud.

+ Theo RAEDSCHELDERS Proper connective differential graded algebras and their geometric realizations 20/04/2020 14:00

A dg algebra $A$ admits a geometric realization if the category of perfect dg $A$-modules can be embedded into the bounded derived category of a smooth projective variety. In this talk, I will first give an overview of Orlov's results on geometric realizations of dg algebras, and then explain how all dg algebras with finite dimensional cohomology, which are moreover concentrated in non-positive degrees, admit such realizations. The proof is based on a generalization of the Auslander algebra of a finite dimensional algebra to the setting of finite-dimensional A-infinity algebras. If time allows, I will discuss several corollaries related to finite-dimensional models, noncommutative motives, and non-Fourier-Mukai functors. This is based on joint work with Alice Rizzardo, Greg Stevenson, and Michel Van den Bergh.

+ Alex Atsushi TAKEDA Integrating non-commutative Calabi-Yau structures 06/04/2020 14:00 https://zoom.us/j/545900254

In this talk I will present some recent developments building on the topic of the paper https://arxiv.org/abs/1605.02721. I will introduce the concept of absolute and relative Calabi-Yau structures on dg categories/algebras defined by Brav and Dyckerhoff, and then show how these structures come from a more general definition of an orientation on a (co)sheaf of categories. This will be a noncommutative version of the usual notion of an orientation on a manifold, and gives the desired Calabi-Yau structures upon integration.

+ Roland BERGER Calcul de Koszul des algèbres préprojectives / Koszul calculus of preprojective algebras 30/03/2020 14:00 https://zoom.us/j/2414213562

Avec Rachel Taillefer (arXiv :1905.07906), nous avons mis en évidence une dualité de 
Poincaré-Van den Bergh des algèbres préprojectives relativement à l'homologie et cohomologie 
de Koszul. Cette dualité est nouvelle quand le graphe est de type Dynkin ADE, ce qui correspond à une

algèbre non Koszul, et elle peut être exploitée en toute généralité en termes de catégorie dérivée.


With Rachel Taillefer  (arXiv :1905.07906), we have exhibited a Poincaré-Van den Bergh duality for

Koszul homology and cohomology of the preprojective algebras. This duality is new when the underlying graph

is of Dynkin type ADE, hence the preprojective algebra is not Koszul, and it can be exploited in full generality

in terms of derived categories.

+ Geoffrey Janssens A Reduction theorem for tau-rigid modules : string algebras ringing 16/03/2020 14:00 exposé par internet via Zoom: https://zoom.us/j/490853589

Motivated by (mutation) deficiencies in classical tilting theory, Adachi, Iyama and Reiten introduced the theory of support tau-tilting modules. In this talk we will be concerned with the problem of determining all support tau-tilting modules (or equivalently all basic two-term silting complexes) for various finite dimensional algebras A over an algebraically closed field. To this end, I will explain a tool that allows to reduce the problem for a given algebra to a more tractable one by repeatedly taking quotients by central elements (in the radical). In practice, it turns out that this process often spits out a string algebra for which I will present an explicit combinatorial description of the support tau-tilting modules. Also various applications, such as tau-tilting finiteness and iterated tilting mutation, to blocks of group algebras and special biserial algebras will be presented.  This is based on joint work with Florian Eisele and Theo Raedschelders.

+ Matthew Pressland Propriétés Calabi-Yau des diagrammes de Postnikov 17/02/2020 14:00

Un diagramme de Postnikov est une collection de brins dans un disque, soumise à certaines règles concernant les croisements des brins. Le diagramme détermine beaucoup d'autres objets et notamment une algèbre amassée. Un théorème récent de Galashin et Lam affirme que cette algèbre est isomorphe à l'anneau des fonctions régulières sur une sous-variété de la grassmannienne dite variété de positroïde. Dans cet exposé, je vais expliquer la construction d'une catégorification de cette algèbre amassée basée sur une propriété de Calabi-Yau d'une autre algèbre (non commutative) associée au diagramme de Postnikov.

+ Peigen Cao The enough g-pairs property of cluster algebras and applications 10/02/2020 14:00

We will talk about the enough g-pairs property of  cluster algebras and its explanations in terms of categories and surfaces.  We will give its applications to d-vectors and characterization for clusters.

+ Simone Virili Morita Theory for Stable Derivators 03/02/2020 14:00
We give a general construction of realization functors for t-structures on the base of a strong stable derivator. In particular, given such a derivator D, a t-structure t=(D≤0,D≥0) on the triangulated category D(1), and letting A=D≤0∩D≥0 be its heart,  we construct a morphism of prederivators 
where Der is the natural prederivator enhancing the derived category of A. Furthermore, we give criteria for this morphism to be fully faithful and essentially surjective. If the t-structure t is induced by a suitably "bounded" co/tilting object, realt is an equivalence. Our construction unifies and extends most of the derived co/tilting equivalences that have appeared in the literature in the last years. 
+ Michela VARAGNOLO Catégorification cohérente de sl(2) affine. 20/01/2020 14:00

Je vais présenter une équivalence de categories abéliennes graduées entre une catégorie de modules pour l’algèbre de Hecke Carquois de type A_1^(1) et la catégorie des faisceaux pervers cohérents sur le conenilpotent de type A. Je ferai ensuite le lien avec les catégorifications de Kashiwara-Kim-Oh-Park et de Cautis-Williams de la cellule ouverte unipotente quantique de type A_1^(1).


The enough g-pairs property of cluster algebras and applications. We will talk about the enough g-pairs property of  cluster algebras and its explanations in terms of categories and surfaces.  We will give its applications to d-vectors and characterization for clusters.

+ The enough g-pairs property of cluster algebras and applications 09/12/2019 14:00
+ Toshiya Yurikusa Denseness of g-vector cones from marked surfaces 02/12/2019 14:00

A triangulation of marked surfaces induces a Jacobian algebra. We study g-vector cones associated with its tau-tilting modules. We determine the closure of the union of g-vector cones associated with all tau-tilting modules. It is equal to the whole space. Our main ingredients are laminations, their shear coordinates and their asymptotic behavior under Dehn twists. The same result holds for gentle algebras by using their geometric realization.

+ Laura FEDELE Déformations d’anneaux de Grothendieck quantiques et algèbres amassées 25/11/2019 14:00

Des déformations d'algèbres amassées avec plusieurs paramètres quantiques (algèbres amassées toroidales) apparaissent naturellement dans l'étude des représentations d’algèbres affines quantiques. Par ailleurs, la construction algébrique de l’anneau de Grothendieck quantique par Hernandez suggère que nous pouvons avoir aussi assez naturellement des déformations avec plusieurs paramètres de ces anneaux (anneaux de Grothendieck toroidaux). Ces objets sont fortement liés; en particulier lorsque les anneaux de Grothendieck fournissent des exemples de catégorification monoïdale d’algèbres amassées. Nous allons construire l’anneau de Grothendieck toroidal pour une algèbre affine quantique simplement lacée et nous allons prouver  que, de manière remarquable, pour une certaine catégorie monoidale C_1, il y a une structure naturelle d’algèbre amassée toroidale. Ce travail est en collaboration avec D. Hernandez.

+ Tomasz PRZEZDZIECKI Quiver Schur algebras and cohomological Hall algebras 18/11/2019 14:00

Quiver Schur algebras are a generalization of Khovanov-Lauda-Rouquier algebras, well known for their role in the categorification of quantum groups. In this talk I will discuss their basic structural properties, as well as their connection to the cohomological Hall algebras defined by Kontsevich and Soibelman.

+ Michael SHAPIRO Noncommutative Pentagram map 04/11/2019 14:00

A pentagram map is a discrete integrable transformation on the space of projective classes of (twisted) n-gons in projective plane. We will discuss a classical and non-commutative version of pentagram map and its integrability properties. 

+ Mattia ORNAGHI Localizations of the category of $A_{\infty}$-categories and Internal Homs 28/10/2019 14:00

In the first part of the talk, we prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital $A_\infty$-categories with respect to the corresponding classes of quasi-equivalences are all equivalent. As an application, in the second part, we give a complete proof of a claim by Kontsevich stating that the category of internal Homs for two dg categories can be described as the category of strictly unital $A_\infty$-functors between them. This is a joint work with Prof. A. Canonaco and Prof. P. Stellari arXiv:1811.07830.

+ Boris SHOIKHET An approach to Deligne conjecture for (higher) monoidal abelian categories 21/10/2019 14:00 001

In this talk, we discuss our approach to ``higher monoidal Deligne conjecture''.
An interest to this statement raised after the proof of Kontsevich formality theorem given by D.Tamarkin. In this case, it says that the cohomological Hochschild complex of any associative algebra A has a structure of a homotopical 2-algebra. The corresponding monoidal abelian category is the category of A-bimodules.
 We found a proof of a more general statement, which works for a general monoidal abelian category. We adapt the approach of Kock and Toen in their ``simplicial Deligne conjecture''. In the linear situation, we replace Segal monoids used by Kock and Toen by rather exotic objects called Leinster monoids. Rectification of Leinster monoids is one of our technical tools.
Another technical tool is the Drinfeld dg quotient and its refined version, which enjoys a nicer monoidal behaviour. If time permits, we discuss some conceptual problems towards a higher-monoidal generalisation of our results.

+ Baptiste ROGNERUD Modules fidèles et équilibrés pour les algèbres de Nakayama 14/10/2019 14:00 001

Les modules fidèles et équilibrés, qui sont parfois appelés ``modules ayant la propriété de double centralisateur'' apparaissent à de nombreux endroits dans la littérature sur la théorie des anneaux comme par exemple dans la dualité de Schur-Weyl et la notion d'algèbre QF1 de Thrall.
 Dans cet exposé, nous allons étudier ces modules pour les algèbres des matrices triangulaires supérieures et plus généralement pour les algèbres de Nakayama. Nous verrons que le nombre de modules fidèles et équilibrés pour l'algèbre des matrices triangulaires supérieures de taille $n$ est le q-analogue de $n!$ en $q=2$. Parmi ces modules, il y a exactement $n!$ modules ayant exactement $n$ facteurs directs indécomposables. Ces derniers semblent particulièrement intéressants car on peut les munir d'une structure de treillis qui étend naturellement le treillis de Tamari.
 Il s'agit d'un travail en commun avec William Crawley-Boevey, Biao Ma et Julia Sauter.

+ Valerio TOLEDANO-LAREDO La R-matrice méromorphe du Yangien 23/09/2019 14:00 001

Drinfeld a montré que la R-matrice universelle du Yangien Yg d’une algebre de Lie semisimple g donne lieu a des solutions rationnelles des equations de Yang-Baxter sur chaque representation irreductible V de dimension finie de Yg. Etonnament, ceci n’est plus le cas si V est réductible, du moins si l’on demande que ces solutions soient naturelles et compatibles avec le produit tensoriel. J’expliquerai que l’on peut par contre obtenir des solutions méromorphes pour tout V. Cette construction se base sur la resommation de la partie abélienne de R, obtenue avec Sachin Gautam, et la réalisation de sa partie triangulaire inférieure comme twist qui conjuge le coproduit standard de Yg en le coproduit de Drinfeld deformé. Travail en commun avec Sachin Gautam et Curtis Wendlandt, basé sur arXiv:1907.03525

+ Alexander ZIMMERMANN Dégénérescence de zéro dans des catégories triangulées 20/05/2019 14:00 001
L'ensemble des structures de module de dimension d sur une algèbre fixée de dimension finie porte une structure de variété affine sur laquelle le groupe linéaire agit. Les orbites correspondent aux classes d'isomorphisme et un module M dégénère vers le module N si N fait partie de l'adhérence de Zariski de l'orbite de M. Zwara et Riedtmann ont caractérisé la dégénérescence de manière purement algébrique, et cette dernière caractérisation possède un analogue évident dans les catégories triangulées. On s'aperçoit que dans des catégories triangulées l'objet zéro peut dégénérer vers des objets non triviaux, chose absurde dans le cas de modules. Nous étudions ce phénomène de manière systématique. Cet exposé est issu d'un travail en commun avec Manuel Saorin.
+ Vyjayanthi CHARI Tensor products and character formulae for HL-modules and monoidal categorification (Projet ERC QAffine) 06/05/2019 14:00 001
In 2009 Hernandez and Leclerc introduced certain tensor subcategories of representation of quantum affine algebras associated with a height function. Under certain conditions on htis function they proved that the corresponding Grothendieck ring admitted the structure of a cluster algebra. In this talk we shall discuss the problem for a general height function in type A and derive character formulae for the prime objects (cluster variables) in the category and also the tensor product rules (exchange relations) for these objects. Finally we shall discuss a resolution of the prime objects in terms of Weyl (standard) modules. The talk is based on joint work with Matheus Brito.
+ Urban JEZERNIK Irrationality of quotient varieties 29/04/2019 14:00 001
The rationality problem in algebraic geometry asks whether a given variety is birational to a projective space. We will gently introduce the problem and take a look at some recent advances, principally in the direction of negative examples constructed via cohomological obstructions. Special focus will be set on quotient varieties by linear group actions.
+ François DUMAS Déformations de Rankin-Cohen d'algèbres polynomiales en théorie des formes modulaires 08/04/2019 14:00 001
Les crochets de Rankin-Cohen définissent une déformation formelle de l'algèbre graduée $M$ des formes modulaires associées à un sous groupe de $SL(2,Z)$. Cette algèbre se plonge dans l'algèbre $Q$ des formes quasi modulaires et dans l'algèbre $J$ des formes de Jacobi faibles. Dans le cas de l'action du groupe modulaire $SL(2,Z)$, les algèbres $M$, $Q$ et $J$ sont des algèbres de polynômes en 2, 3 et 4 variables respectivement, engendrées par des fonctions de références (séries d'Eisenstein, fonction de Weierstrass,...). Cela permet d'introduire des méthodes algébriques de construction et de classification de déformations de Rankin-Cohen sur $M$, $Q$ et $J$, que l'on présentera lors de cet exposé. Il s'agit d'un travail en collaboration avec Y. Choie, F. Martin et E. Royer.
+ Luc PIRIO Polylogarithmes, tissus et algèbres amassées. 01/04/2019 14:00 001
Il s’agira d’expliquer comment, via des méthodes issues de la ``géométrie des tissus’’, j’ai pu obtenir des résultats intéressants sur les équations fonctionnelles des polylogarithmes, en liaison avec la théorie des algèbres amassées.
+ Martina LANINI The Steinberg-Lusztig tensor product theorem for abstract Fock space (Projet ERC QAffine) 18/03/2019 14:00 001
The abstract Fock space, constructed in joint work with A.Ram and P.Sobaje, is a combinatorial gadget which generalises Lecler-Thibon's realisation of the classical Fock Space to any type, and encodes decomposition numbers for quantum groups at roots of unity. In this talk I will discuss joint work with Arun Ram, in which we establish the analogue of the Steinberg-Lusztig Tensor product Theorem for abstract Fock space. This result has several consequences, such as a new proof of the Casselman-Shalika formula, and a character formula for a certain class of modules for affine Kac-Moody algebras at a negative level.
+ Christophe REUTENAUER Nombres de Markoff et palindromes 11/03/2019 14:00 001
Après un survol de la théorie de Markoff sous ses deux aspects (formes quadratiques et fractions continues), on verra comment certains palindromes sont liés à cette théorie
+ Pedro TAMAROFF The Tamarkin-Tsygan calculus of an algebra à la Stasheff 04/03/2019 14:00 001
For a commutative smooth $k$-algebra $A$, the Hochschild-Konstant-Rosenberg theorem identifies Hochschild homology of $A$ with forms $\Lambda^*(\Omega(A))$ on $A$ and Hochschild cohomology of $A$ with polyvector fields $\Lambda^*(Der(A))$ on $A$. These two new spaces have a very rich algebraic structure coming from the geometric Cartan calculus on smooth varieties: a Lie bracket on fields, an exterior product on forms and polyvector fields, an interior product of forms with fields and a deRham differential. There is a non-commutative counterpart to this story for an associative algebra $A$, introduced by B. Tsygan and D. Tamarkin, now called the Tamarkin-Tsygan calculus of $A$. I will explain how to compute it through a dg model of $A$, by giving first a model for the spaces of forms and fields that give rise to homology and cohomology, and then provide explicit formulas for the Gerstenhaber bracket and cup product on fields, the contraction of forms by fields and the boundary of $A$. Connes on forms. This extends the work of J. Stasheff - who originally gave a definition of the Gerstenhaber bracket of $A$ intrinsic to the category of $dg$ algebras - to the whole Tamarkin-Tsygan calculus of an algebra.
+ Dylan ALLEGRETTI Relating stability conditions and cluster varieties 25/02/2019 14:00 001
I will describe the relationship between two spaces associated to a quiver with potential. The first is a complex manifold parametrizing Bridgeland stability conditions on a triangulated category, and the second is a cluster variety with a natural Poisson structure. For quivers of type A, I will describe a local biholomorphism from the space of stability conditions to the cluster variety. The existence of this map follows from results of Sibuya in the classical theory of ordinary differential equations.
+ Hiroyuki NAKAOKA Finite gentle repetitions of gentle algebras and their Avella-Alaminos--Geiss invariants 18/02/2019 14:00 001
We consider a repetition procedure to construct gentle algebras out of a given gentle bound quiver. I would like to show how their Avella-Alaminos--Geiss invariants are determined by those of the original one, and how this repetition can be expressed by an upper-triangular matrix algebra. I will also mention a few cases where this procedure preserves derived equivalences.
+ Michèle VERGNE Conditions de Horn pour les positions de Schubert de sous-représentations de carquois générales 11/02/2019 14:00 001
Nous donnons des conditions inductives qui caractérisent les positions de Schubert de sous-représentations de la représentation générale d'un carquois. Nos résultats généralisent le critère de Horn pour l'intersection des variétés de Schubert dans des Grassmanniennes et viennent raffiner la caractérisation par Schofield des vecteurs dimension de sous-représentations générales. Nous démonstrations sont inspirées par l'argument de Schofield ainsi que par la démonstration géométrique par Belkale de la conjecture de saturation. Travail en commun avec Velleda Baldoni et Michael Walter.
+ Michel DUBOIS-VIOLETTE Géométrie quantique exceptionnelle et physique des particules 04/02/2019 14:00 001
Tout d’abord nous rappelons et expliquons l’analyse de Jordan, von Neumann et Wigner établissant que les algèbres de Jordan euclidiennes de dimension finie sont les algèbres d’observables des systèmes quantiques finis, c’est-à-dire les analogues quantiques des algèbres de fonctions réelles sur les ensembles finis. Ensuite nous décrivons en détail notre approche associant l’algèbre de Jordan exceptionnelle des matrices hermitiennes 3 x 3 octonioniques à la classification des particules fondamentales de matière, de leur groupe de symétrie et de leurs interactions.
+ Thierry LAMBRE Méthodes de géométrie différentielle en théorie algébrique des nombres 28/01/2019 14:00 001
Les notion de connexion et de courbure sont centrales en géométrie différentielle. Dans les années 80, A. Connes et M. Karoubi, les ont utilisées dans un cadre algébrique pour construire des caractères de Chern de source la K-théorie algébrique, de but diverses homologies (de Hochschild, cyclique, etc. ). Dans cet exposé, nous montrerons comment il est possible de construire une structure de groupes sur l'ensemble des connexions d'un anneau de Dedekind et comment on peut exploiter ce groupe des connexions en théorie algébrique des nombres (travail en collaboration avec J. Berrick, Yales-NUS).
+ Peter JØRGENSEN Model categories of quiver representations 21/01/2019 14:00 001
(report on joint work with Henrik Holm) Let R be a k-algebra. Given a cotorsion pair (A,B) in Mod(R), Gillespie's Theorem shows how to construct a model category structure on C(Mod R), the category of chain complexes over Mod(R). There is an associated homotopy category H. If (A,B) is the trivial cotorsion pair (projective modules, everything), then H is the derived category D(Mod R). Several other important triangulated categories can also be obtained from the construction. Chain complexes over R are the Mod(R)-valued representations of a certain quiver with relations: Linearly oriented A double infinity modulo the composition of any two consecutive arrows. We show that Gillespie's Theorem generalises to arbitrary self-injective quivers with relations, providing us with many new model category structures.
+ Zhengfang WANG Gerstenhaber algebra structure on the Tate-Hochschild cohomology 14/01/2019 14:00 001
The Tate-Hochschild cohomology of a singular space X is defined as the graded endomorphism ring of the diagonal inside the singularity category of X x X. Singularity categories were introduced by Buchweitz in representation theory and then rediscovered by Orlov in algebraic geometry and homological mirror symmetry. By Keller's very recent result, the Tate-Hochschild cohomology of an algebra is isomorphic to the Hochschild cohomology of its dg singularity category. In this talk, we construct an explicit complex to compute the Tate-Hochschild cohomology. We prove that there is a natural action of the little 2-discs operad on this complex. In particular, the Tate-Hochschild cohomology is a Gerstenhaber algebra. We also talk about a joint work with M. Rivera that the Tate-Hochschild cohomology of a simply-connected manifold M recovers the Rabinowitz-Floer homology of the unit disc cotangent bundle on M.
+ Vincent PILAUD Sur les type cones des éventails de g-vecteurs 17/12/2018 14:00 001
Dans une prépublication récente, Bazier-Matte -- Douville -- Mousavand -- Thomas -- Yildirim construisent toutes les réalisations polytopales des éventails des g-vecteurs des algèbres amassées de type fini pour des graines initiales acycliques. Cet exposé expliquera la raison géométrique cachée derrière leur construction et proposera une preuve alternative de leur résultat. Plus généralement, on discutera le type cone (en d'autre termes, l'espace de toutes les réalisations polytopales) des éventails de g-vecteurs de certains complexes simpliciaux dans la grande famille des complexes amassés (complexes amassés de type fini depuis n'importe quel graine initiale, complexes platoniques des algèbres aimables, associaèdres de graphes). Travail en commun avec Arnau Padrol, Yann Palu et Pierre-Guy Plamondon.
+ Valentin OVSIENKO What is... un nombre rationnel quantique? 10/12/2018 14:00 001
Il n’y a pas à nos jours de réponse à cette question dans la littérature. On propose une réponse basée sur des propriétés combinatoires des fractions continues. L’idée est de déformer les développements des rationnels en fractions continues de façon à preserver le lien avec la géométrie hyperbolique et le groupe modulaire PSL(2,Z). La définition des q-rationnels étend naturellement celle des q-entiers et fait apparaitre des polynômes à coefficients entiers avec comme principales propriétés, des phénomènes de positivité totale. On propose une interpretation énumérative des coefficients de ces polynômes en termes de representations des carquois. On remarque aussi un lien avec le polynôme de Jones. Il s’agit d’un travail en commun avec Sophie Morier-Genoud.
+ Gustavo JASSO On the Dold-Kan correspondence 03/12/2018 14:00 !314
The classical Dold-Kan correspondence is an explicit equivalence of categories between the category of simplicial abelian groups and the category of connective chain complexes of abelian groups. There is a recent variant of this correspondence, due to Dyckerhoff, where the category of abelian groups is replaced by the $(\infty,2)$-category of stable $\infty$-categories. In this talk I will discuss, using only rudiments of $\infty$-category theory, common aspects of these correspondences and explain how these fit within the conjectural framework of categorified homological algebra. The talk is based on join work in progress with Tobias Dyckerhoff and Tashi Walde.
+ Emmanuel LETELLIER Représentations des carquois sur des algèbres de Frobenius 26/11/2018 14:00 !421
Dans cet exposé on étudiera les représentations localement libres d'un carquois $Q$ sur une algèbre de Frobenius commutative $R$ (ex : algèbre de polynômes tronqués) en utilisant les transformations de Fourier. On verra comme cette transformation de Fourier permet de relier les représentations de l'algèbre preprojective de $Q$ sur $R$ avec les représentations de $Q$ sur l'algèbre de Frobenius $R[t]/(t^2)$. On donnera une classification des paires $(Q,R)$ pour lesquelles il y a un nombre fini de classes d'isomorphisme d'objets indécomposables.
+ Baptiste ROGNERUD Les ensembles ordonnés de Tamari sont Calabi-Yau fractionnaires 19/11/2018 14:00 001
Les ensembles ordonnés de Tamari sont des ordres (partiels) classiques et bien étudiés. Ils apparaissent de façon naturelle en théorie des représentations des algèbres comme ensemble ordonnés des modules basculants sur un carquois équiorienté de type $A$ mais aussi comme ensemble cambrien du même type. Chapoton a été un des premiers à se rendre compte que la théorie des représentations des algèbres d'incidences de ces ensembles est en elle-même extrêmement fascinante. Il démontre en 2004 que les matrices de Coxeter des ensembles ordonnés de Tamari sont périodiques. Peu de temps après, il conjecture un résultat plus fort : les catégories dérivées bornées des algèbres d'incidences des ensembles ordonnés de Tamari sont Calabi-Yau fractionnaires. c'est-à-dire qu'une certaine puissance de leur foncteur de Serre est isomorphe à un foncteur de décalage. Dans cet exposé, après avoir donné des exemples élémentaires d'ensembles ordonnés Calabi-Yau fractionnaires, je présenterai les ingrédients principaux de la démonstration de cette conjecture.
+ Adrien BROCHIER Dualisabilité des catégorie tensorielles tressée 12/11/2018 14:00 !005
En théorie de Morita, les algèbres associaitves, bimodules et morphismes de bimodules forment naturellement une 2-catégorie. Chaque algèbre définit alors une certaine théorie topologique des champs (TFT) en dimension 1 à valeur dans cette 2-catégorie, et modulo des hypothèses de finitudes restrictives on obtient une TFT en dimension 2. La valeur de ces TFT sur des variétés bien choisies retrouve et organise un certain nombre de structures et de propriétés en théorie des représentations (par exemple, l'image du cercle donne la ``trace'' de l'algèbre, ou l'homologie de Hochschild dans un cadre dérivé, les conditions de finitudes supplémentaires imposent la semi-simplicité etc..). Dans cet exposé, j'esquisserai une variante de cette construction pour les catégories tensorielles et tensorielles tressées. Là encore, via l'hypothèse du cobordisme de Baez--Dolan récemment prouvée par Lurie, on obtient des TFT's en dimension 2,3 ou 4 suivant les hypothèses de finitudes imposées. On discutera un certain nombre d'applications, notamment en appliquant cette construction à la catégorie des représentations d'un groupe quantique. Cet exposé est basé sur une collaboration avec D. Ben-Zvi, D. Jordan et N. Snyder.
+ Laura FEDELE Generators for quantum finite W-algebras in type A 05/11/2018 14:00 !005
A major contribution to the theory of quantum finite W-algebras in type A comes from the work of J. Brundan and A. Kleshchev who, investigating the relationship between W-algebras and Yangians, achieved important results concerning both their structure and their representation theory. In this framework, for a quantum finite W-algebra in type A, associated to any nilpotent element and arbitrary good grading, we can construct a matrix of Yangian type L(z) which encodes its generators and relations, generalizing the results of A. De Sole, V. Kac and D. Valeri for classical affine W-algebras. We can then express L(z) in a nicer form: when the good grading is associated to a pyramid that is aligned to the right, we use a recursive formula to explicitly construct a matrix W(z) which provides us with a finite set of generators for the W-algebra satisfying Premet's conditions, and prove that the matrix L(z) can be obtained as a generalized quasideterminant of W(z). Finally, we explain how to generalize these results to an arbitrary good grading (and an arbitrary choice of an isotropic subspace), using fundamental results about the structure of quantum finite W-algebras due to W.L. Gan and V. Ginzburg, and J. Brundan and S. Goodwin. This is a joint work with A. De Sole and D. Valeri.
+ Andrea PASCUAL Self-injective Jacobian algebras from Postnikov diagrams 29/10/2018 14:00 001
A Postnikov diagram is a collection of curves in a disk subject to some axioms depending on two integers $1\leq k\leq n$. The arising combinatorics is related to that of the cluster structure of the coordinate ring of the Grassmannian of $k$-subspaces of $\mathbb C^n$. To a Postnikov diagram one can associate a finite-dimensional Jacobian algebra, by work of Oh-Postnikov-Speyer. Baur-King-Marsh later proved that the Jacobian algebra is isomorphic to the stable endomorphism algebra of a cluster tilting object in a 2-Calabi-Yau category introduced by Jensen-King-Su. In this talk I will explain how to characterise self-injectivity of this Jacobian algebra combinatorially. I will also show some new examples of planar self-injective quivers with potential one gets in this way (the terminology is that of Herschend-Iyama), and explain a connection to 2-dimensional Auslander-Reiten theory.
+ Lucie JACQUET-MALO Réalisation géométrique des catégories amassées supérieures et réduction d'Iyama-Yoshino 22/10/2018 14:00 !421
Nous allons démontrer qu'une sous-catégorie de la catégorie $m$-amassée de type $\tilde{D_n}$ est isomorphe à une catégorie construite à partir d'arcs dans un $(n-2)m$-gone muni de deux $(m-1)$-gones en son centre. On démontre que la mutation de carquois colorés au sens de Buan et Thomas est compatible avec la mutation des objets $m$-amas-basculants, ainsi qu'avec le flip des $(m+2)$-angulations. Dans cet exposé, nous allons étudier les réalisations géométriques des catégories $m$-amassées de type Dynkin $A$, $D$, $\tilde{A}$ et $\tilde{D}$. On démontre dans ces quatre cas qu'il y a une bijection entre les $(m+2)$-angulations et les classe d'isomorphie des objets basiques $m$-amas-basculants. Ainsi, les flips des $(m+2)$-angulations correspondent aux mutations des objets $m$-amas-basculants. La stratégie pour prouver ceci est de démontrer qu'effectuer la réduction d'Iyama-Yoshino revient à couper le long d'un arc dans la réalisation géométrique. On peut ainsi espérer généraliser ce résultat aux surfaces de Riemann dans le cas $m$-amassé.
+ Sondre KVAMME La catégorie des singularités d'une sous-catégorie dZ-amassée basculante 15/10/2018 14:00 001
La catégorie des singularités d'un anneau noethérien a été introduite par Buchweitz comme un invariant utile d'anneaux. C'est une catégorie triangulée qui peut, par exemple, détecter si la dimension globale de l'anneau est finie. Le but de cet exposé est d'expliquer un lien entre la théorie d'Auslander-Reiten supérieure qui a été introduite par Iyama, et la catégorie des singularités. Plus précisément, pour une catégorie exacte ayant assez de projectifs et avec une sous-catégorie dZ-amassées basculante, la catégorie des singularités possède une sous-catégorie dZ-amassées basculante. Nous allons aussi parler un peu de la demonstration de cette affirmation, qui utilise la description de la catégorie des singularités comme l'extension d'une catégorie co-suspendue obtenue par Keller et Vossieck.
+ François BERGERON Modules de polynômes harmoniques diagonaux 08/10/2018 14:00 001
Depuis le début des années 1990, l’étude des polynômes symétriques de Macdonald, et des opérateurs pour lesquels ils sont des fonctions propres, a entraîné un grand intérêt pour l’étude des $S_n$-modules de polynômes harmoniques diagonaux, où $S_n$ est le groupe symétrique. Rappelons que ces polynômes harmoniques sont les polynômes en plusieurs jeux de $n$-variables qui sont annihilés par tout opérateur de dérivation invariant pour l’action de $S_n$, c.-à-d celle qui permute “diagonalement” chacun des jeux de variables. Le lien de ces modules de polynômes harmoniques avec les polynômes de Macdonald apparaît lorsqu’on cherche a décrire explicitement leur caractère gradué. D’autre part, via les algèbres de Hall elliptiques, une vaste expansion de cette problématique s’est mise en place récemment. Cependant, il y manquait jusqu’ici tout le volet théorie de la représentation analogue. Après avoir bien rappelé le contexte, nous allons décrire les modules que nous proposons pour rendre compte de cette généralisation, et esquisser les très intéressantes propriétés qu’ils semblent avoir.
+ Tristan BOZEC Composantes irréductibles du cône global nilpotent (Projet ERC QAffine) 11/06/2018 14:00 001
Étant donnée une courbe $X$ de genre $g$, le champ de modules des faisceaux de Higgs de rang r et degré d est de dimension $2(g-1)r^2$. Il peut être vu comme le champ cotangent au champ des faisceaux cohérents de type $(r,d)$ sur $X$, et Laumon a prouvé que le sous-champ des paires de Higgs nilpotentes est Lagrangien. Ce sous-champ est un analogue global du cône nilpotent, et c'est la fibre au-dessus de $0$ de l'application de Hitchin. Il est très singulier, et une étape intéressante dans sa compréhension consiste en l'étude de ses composantes irréductibles. Cette étude est notamment motivée par un résultat reliant le nombre des composantes stables (relativement à la pente usuelle) à la valeur en $1$ du polynôme de Kac associé au carquois à un sommet et $g$ boucles (conjecture de Hausel, Letellier, Rodriguez Villegas prouvée par Mellit). Je donnerai une description combinatoire des composantes de ce cône, et expliquerai lesquelles subsistent dans le lieu semi-stable.
+ Pu ZHANG Frobenius-Perron theory of endofunctors 04/06/2018 14:00 001
We introduce the Frobenius-Perron dimension of an endofunctor of a k-linear category and provide some applications. This talk is based on preprint \href{https://arxiv.org/pdf/1711.06670.pdf}{https://arxiv.org/pdf/1711.06670.pdf}.
+ Auguste HÉBERT Complétions et centres des algèbres d’Iwahori-Hecke pour les groupes de Kac-Moody sur les corps locaux 28/05/2018 14:00 001
Soit $G$ un groupe réductif sur un corps local. Les algèbres de Hecke de $G$ sont un outil important pour l’étude des représentations de $G$. Ces algèbres sont associées à chaque sous-groupe ouvert compact de $G$. Deux algèbres jouent un rôle particulièrement important : l’algèbre de Hecke $H_s$ sphérique, associée à un compact maximal et celle d’Iwahori-Hecke $H_i$, associée au sous-groupe d’Iwahori. Les groupes de Kac-Moody sont des généralisations des groupes réductifs. Grâce aux travaux de Braverman, Kazhdan et Patnaik puis à ceux de Bardy-Panse, Gaussent et Rousseau, ces deux algèbres ont été définies dans le cas des groupes de Kac-Moody sur des corps locaux. Dans cet exposé, on donnera la définition de ces algèbres et on étudiera le centre de $H_i$. Lorsque $G$ est réductif, des théorèmes de Bernstein et Satake montrent que le centre de l’algèbre de $H_i$ est isomorphe à $H_s$. Lorsque $G$ n’est plus réductif, le centre de $H_i$ est plus ou moins trivial. On peut alors « compléter » $H_i$ de manière à ce que son centre soit isomorphe à $H_s$.
+ Anthony JOSEPH Canonical S-graphs, Catalan numbers and convexity 14/05/2018 14:00 001
The notion of an $S$-graph is introduced. These are not unique but for each positive integer there is a canonical family. Each member of the family is given by the natural ordering on n distinct positive integers. The total number of distinct canonical $S$-graphs is not n! but the Catalan number $C(n)$. Each member of the family gives a set of $2^n$ points in $Q^n$ which turn out to be the extremal points of a convex set.
+ Tsukasa ISHIBASHI Cluster realizations of Coxeter groups and their relations with higher Teichmuller spaces (Projet ERC QAffine) 07/05/2018 14:00 001
For a Coxeter group $W$ satisfying some mild conditions, we construct a family of seeds such that the corresponding cluster modular group contains $W$ as a subgroup. It is a generalization of the construction for type $A_n$ given by Inoue-Lam-Pylyavskyy. Moreover, we show that one of our seed for type $A_n$ is mutation- equivalent to the $SL_{n+1}$-higher Teichmuller seed for the punctured disk with even number of marked points on its boundary. In particular $W(A_n)$ acts on the moduli space of decorated (twisted) local systems. We show that this action coincides with that given by Goncharov-Shen, which is also a cluster action. This talk is based on a joint work with Rei Inoue.
+ Michel van den Bergh A k-linear triangulated category without a model 30/04/2018 14:00 001
We give an example of a triangulated category, linear over a field of characteristic zero, which does not carry a DG-enhancement. The only previous examples of triangulated categories without a model have been constructed by Muro, Schwede and Strickland. These examples are however not linear over a field. This is joint work with Alice Rizzardo.
+ Alexey SEVASTYANOV Zhelobenko operators, Schubert cells and q-W algebras 16/04/2018 14:00 001
In the beginning of the 80th Zhelobenko suggested a formula for a projection operator onto the subspace of singular vectors for modules from the BGG category O for a complex semisimple Lie algebra. This projection operator and some its modifications called Zhelobenko operators are related to the problem of finding an explicit description for the space of invariant regular functions with respect to the conjugation action of the unipotent radical of a semisimple algebraic group on the Borel subalgebra. In this talk I shall discuss a similar construction in case of the so-called q-W algebras which are related to the category of generalized Gelfand-Graev representations for quantum groups. The underlying geometry in this case is the geometry of the conjugation action of certain unipotent groups on Schubert cells. Using Zhelobenko operators I shall suggest an explicit description for generators of Poisson q-W algebras. Surprisingly, the results that will be presented in this talk have no direct analogues for complex semisimple Lie algebras and for ordinary W-algebras associated to them.
+ Yann PALU Complexe platonique des algèbres aimables 09/04/2018 14:00 001
Le complexe platonique (non-kissing complex) est un complexe simplicial introduit en combinatoire par T. McConville. Après avoir exposé les notions combinatoires nécessaires, je présenterai une interprétation algébrique de ce complexe à l'aide de la théorie des représentations d'algèbres. J'expliquerai ensuite comment généraliser le complexe platonique à la classe des algèbres aimables, ainsi que quelques conséquences de ce résultat. Il s’agit d’un travail en commun avec Vincent Pilaud et Pierre-Guy Plamondon.
+ Lara BOSSINGER Toric degenerations from representation theory, tropical geometry and cluster algebras (Projet ERC QAffine) 26/03/2018 14:00 001
In this talk I will explain how toric degenerations arise from the tropicalization of a (projective) variety. In the context of varieties that are interesting from a representation theoretic point of view (e.g. Grassmannians or flag varieties) I will explain a construction of toric degenerations due to Fang, Fourier, and Littelmann called birational sequences and compare to degenerations obtained from the cluster structure on these varieties. I will present many examples and some results on how these constructions are related. For example, I will present computational results on the tropicalization of the full flag variety for n=4 and 5 and compare the obtained toric degenerations to some classical degenerations from representation theory (string polytopes and the FFLV polytope) that arise in the context of birational sequences.
+ Julian KULSHAMMER Existence and uniqueness of exact Borel subalgebras 12/03/2018 14:00 001
Quasi-hereditary algebras and their infinite analogues, highest weight categories, appear frequently in many areas of representation theory. In joint work with S. Koenig and S. Ovsienko, we showed that every quasi-hereditary algebra can up to Morita equivalence be obtained as the dual of a coring object in the tensor category of bimodules over a directed algebra, the exact Borel subalgebra. Under an additional assumption, the exact Borel subalgebra as well as the coring object are in fact unique up to isomorphism. This is joint work with V. Miemietz.
+ Amnon YEKUTIELI The Derived Category of Sheaves of Commutative DG Rings 26/02/2018 14:00 001
In modern algebraic geometry we encounter the notion of derived intersection of subschemes. This is a sophisticated way to encode what happens when two subschemes $Y_1$ and $Y_2$ of a given scheme X intersect non-transversely. The classical intersection multiplicity can be extracted from the derived intersection. When the ambient scheme X is affine, it is not too hard to describe the derived intersection, by taking flat DG ring resolutions of the structure sheaves of the subschemes $Y_1$ or $Y_2$. This also works when the scheme X is quasi-projective. However, derived intersections in more general schemes X could only be treated using the very difficult homotopical methods of derived algebraic geometry. Several months ago I discovered a ``cheap'' way to construct flat resolutions of sheaves of rings. The resolutions are by semi-pseudo-free sheaves of DG rings. The main advantage is that the geometry does not change: all the action takes place on the original topological space X. Using semi-pseudo-free resolutions it is possible to produce derived intersections as above. It is also possible to get a direct presentation of the cotangent complex of a scheme (at least in characteristic 0). Presumably the derived adic completion of Shaul, so far studied only in the affine case, could be globalized using our our methods. Lastly, the semi-pseudo-free resolutions give rise to a congruence on the category of sheaves of commutative DG rings on the space X, that we call relative quasi-homotopy. The functor from the homotopy category to the derived category turns out to be a faithful right Ore localization. This fact gives tight control on the derived category. It should be noted that in this situation there does not seem to exist a Quillen model structure, so the traditional approaches would fail. In the talk I will explain the various ideas listed above. More details can be found in the eprint \href{http://front.math.ucdavis.edu/1608.04265}{arxiv:1608.04265}.
+ Travis SCHEDLER Résolutions symplectiques des variétés de carquois et des caractères (Projet ERC QAffine) 19/02/2018 14:00 001
Nous allons expliquer une classification des variétés de carquois (Nakajima) qui admettent une résolution symplectique, et similairement pour les variétés des caractères d’une surface de Riemann (espace moduli des systèmes locales). Nous expliquons également un résultat parallèle pour les espaces moduli de Higgs de A. Tirelli (doctorant). Ce travail est en collaboration avec G. Bellamy.
+ Toshiki NAKASHIMA Geometric crystals on cluster varietie 05/02/2018 14:00 001
The notion of geometric crystal was initiated by A.Berenstein and D.Kazhdan to consider certain geometric analogue to the Kashiwara's crystal base theory. Their structures are described by rational maps and rational functions. If all these rational maps are ``positive'', such geometric crystals are called ``positive'' and they can be tranfered to the ``Langlands dual crystal bases'' by tropicalization/ultra-discretization procedure. V.Fock and A.Goncharov defined certain pair of varieties (A,X), called ``cluster ensemble'' which is obtained by glueing algebraic tori using the ``A-mutations and X-mutations'' respectively. They gave the conjectures on ``tropical duality'' between cluster ensemble A-variety and X-variety (called Fock-Goncharov conjectures). We shall define the positive geometric crystal structure on cluster varieties and then obtain the resulting tropicalized crystals, which will be a guide to understand the Fock-Goncharov conjectures in terms of crystal base theory. Finally, we shall show some compatibility of geometric crystal structures on A-variety and X-variety in the classical type A case.
+ Bruno VALLETTE Ubiquité du groupe de jauge homotopique 22/01/2018 14:00 001
La théorie de déformation des algèbres à homotopie près est codée par une algèbre de Lie de convolution. Comme cette dernière provient d’une structure pré-Lie, on peut l’intégrer avec des formules plus simples que celle de Baker—Campbell—Hausdorff. Ceci permet de décrire efficacement le groupe de jauge homotopique dont on montrera que l’action donne “toutes” les constructions fonctorielles de l’algèbre homotopique : théorème de transfert homotopique, torsion des structures par des éléments de Maurer—Cartan, hiérarchie de Koszul, etc.
+ Christof GEISS Crystal graphs and semicanonical functions for symmetrizable Cartan matrices. 15/01/2018 14:00 001
In joint work with B. Leclerc and J. Schröer we propose a 1-Gorenstein algebra $H$, defined over an arbitrary field $K$, associated to the datum of a symmetrizable Cartan Matrix $C$, a symmetrizer $D$ of $C$ and an orientation $\Omega$. The $H$-modules of finite projective dimension behave in many aspects like the modules over a hereditary algebra, and we can associate to $H$ a generalized preprojective algebra $\Pi$. If we look, for $K$ algebraically closed, at the varieties of representations of $\Pi$ which admit a filtration by generalized simples, we find that the components of maximal dimension provide a realization of the crystal $B_C(-\infty)$. For K being the complex numbers we can construct, following ideas of Lusztig, an algebra of constructible functions which contains a family of ``semicanonical functions'', which are naturally parametrized by the above mentioned components of maximal dimensions. Modulo a conjecture about the support of the functions in the ``Serre ideal'' those functions would yield a semicanonical basis of the enveloping algebra $U(n)$ of the positive part of the Kac-Moody Lie algebra $g(C)$.
+ Ryo FUJITA Affine highest weight categories and quantum affine Schur-Weyl duality of Dynkin quiver types (Projet ERC QAffine) 08/01/2018 14:00 001
The notion of affine highest weight category introduced by Kleshchev is an ``affine'' generalization of the notion of highest weight category and axiomatizes certain homological structures of some non-semisimple abelian categories of Lie theoretic origin. By comparing such structures, we can see that Kang-Kashiwara-Kim's generalized quantum affine Schur-Weyl duality functor associated to each Dynkin quiver $Q$ gives an equivalence of monoidal categories between the module category of the corresponding quiver Hecke algebra and Hernandez-Leclerc's monoidal subcategory $C_Q$ inside the module category of the quantum loop algebra.
+ Sondre KVAMME A generalization of the Nakyama functor 11/12/2017 14:00 001
We define the notion of a Nakayama functor relative to an endofunctor on an abelian category, which generalizes the classical Nakayama functor for finite-dimensional algebras. We study this concept from the viewpoint of Gorenstein homological algebra. In particular, we obtain a generalization of the equality of the left and right injective dimension of a finite-dimensional Iwanaga-Gorenstein algebra. We will illustrate the constructions and results on specific examples.
+ Benjamin ENRIQUEZ Correspondance de Riemann-Hilbert et groupes de tresses. (Projet ERC QAffine) 27/11/2017 14:00 001
Soit $\mathrm{PB}_{0,n}$ le groupe des tresses pures à $n$ brins sur la sphère de dimension 2. Un résultat classique est le calcul de l'algèbre de Lie de son complété pro-unipotent. Ce résultat peut se montrer à l'aide de la correspondance (RH) entre les catégories, d'une part des systèmes locaux pro-unipotents sur l'espace de configuration de $n$ points dans $\mathbf P^1(\mathbb C)$, d'autre part des fibrés vectoriels à connection plate pro-unipotents sur le même espace (Deligne). On sait aussi faire le calcul analogue dans le cas du groupe $\mathrm{PB}_{1,n}$ des tresses pures à $n$ brins sur le tore de dimension 2 (Bezrukavnikov, Calaque-Etingof-E.). Nous montrons comment une démonstration fondée sur la correspondance RH peut être construite dans ce cas, en utilisant une surface $E^\sharp$ associée à une courbe elliptique complexe $E$, espace total d'un fibré sur $E$ en espaces affines. (Travail commun avec P. Etingof.)
+ Peng SHAN Cohomologie Equivariante des espaces de Calogero-Moser 20/11/2017 14:00 001
On expliquera comment calculer la cohomologie équivariant des espaces de Calogero-Moser lisses en utilisant représentations des algèbres de Cherednik rationnelles. On donnera aussi une application pour la cohomologie équivariante de certains résolutations symplectiques. Il s'agit un travail en commun avec Cédric Bonnafé.
+ Osamu IYAMA Representation theory of Geigle-Lenzing complete intersections 06/11/2017 14:00 001
A Geigle-Lenzing complete intersection is a generalization of weighted projective lines of Geigle and Lenzing. We study the stable category of Cohen-Macaulay modules and the derived category of coherent sheaves on the corresponding projective space. They are equivalent to the derived categories of certain finite dimensional algebras. In this talk, we calculate global dimension of these algebras by using Tate’s DG algebra resolution for complete intersections. As an application, we discuss when these categories are equivalent to the derived categories of algebras with small global dimension. This is a joint work with Herschend, Minamoto and Oppermann.
+ Bernard LECLERC La formule de Caldero-Chapoton pour les algèbres amassées anti-symétrisables de type fini (Projet ERC QAffine) 23/10/2017 14:00 001
Il s'agit d'un travail en commun avec C. Geiss et J. Schröer. Nous généralisons la formule de Caldero-Chapoton aux algèbres amassées anti-symétrisables de type fini. Pour cela nous remplaçons les catégories de représentations des carquois de Dynkin par les catégories de modules localement libres sur les algèbres $H(C,D)$ introduites dans nos travaux antérieurs.
+ Hironori OYA Twist automorphisms and Chamber Ansatz formulae for quantum unipotent cells 16/10/2017 14:00 001
Berenstein, Fomin and Zelevinsky introduced biregular automorphisms, called twist automorphisms, on unipotent cells in their study of total positivity criteria. These automorphisms are essentially used for describing the inverses of specific embeddings of tori into unipotent cells, and the resulting descriptions are called the Chamber Ansatz. In this talk, I explain a quantum analogue of their story. Namely, we construct twist automorphisms on arbitrary quantum unipotent cells and provide a quantum analogue of the Chamber Ansatz formulae. We also study our quantum analogues from the viewpoint of the quantum cluster algebra structures on quantum unipotent cells, which are deduced by Geiss- Leclerc-Schroer and Goodearl-Yakimov. A part of this talk is based on joint work with Yoshiyuki Kimura.
+ Patrick DEHORNOY Réduction des multifractions pour les groupes d'Artin-Tits 09/10/2017 14:00 001
Un résultat classique de O. Ore affirme que, si $M$ est un monoïde simplifiable dans lequel deux éléments quelconques admettent un plus petit commun multiple, alors tout élément du groupe enveloppant $U(M)$ de $M$ peut être représenté de façon unique comme une fraction irréductible sur M. On étend ce résultat en affaiblissant la condition sur l'existence des multiples communs, au prix de considérer des sortes de fractions itérées (``multifractions''). Lorsque le monoïde de base $M$ admet une famille de Garside finie, ceci mène à un algorithme d'un type nouveau (mais reminiscent de l'algorithme de Dehn pour les groupes hyperboliques) pour le problème de mot du groupe $U(M)$. Cette méthode est en défaut pour certains monoïdes, mais on conjecture qu'elle s'applique à tous les monoïdes d'Artin-Tits. Réduction des multifractions pour les groupes d'Artin-Tits.
+ Luis PARIS Groupes d'Artin, symétries, et représentations linéaires 12/06/2017 14:00 001
Cet exposé est basé sur un travail en collaboration avec Olivier Geneste et Jean-Yves Hée. Une question populaire sur les groupes de tresses fut pendant longtemps de déterminer si ces groupes sont linéaires. Une réponse (positive) fut donnée par Bigelow et Krammer à la fin des année 90. La construction de Krammer fut rapidement étendue aux groupes d'Artin simplement lacés de type sphérique par Cohen--Wales et Digne, puis à tous les groupes d'Artin simplement lacés par moi-même. Reste à savoir comment étendre cette construction aux autres groupes, ceux qui ne sont pas simplement lacés. On peut trouver une réponse partielle à cette question dans des travaux de Digne et Castella sur les symétries des représentations. Cette réponse couvre les groupes de type $B_n$, $F_4$ et $G_2$. Nous raconterons cette histoire plus en détail et montrerons comment étendre les idée de Digne et quelles sont les limites de cette construction.
+ Patrick LE MEUR Algèbres Calabi-Yau tordues 22/05/2017 14:00 001
Une algèbre Calabi-Yau (CY) tordue est une algèbre (associative, unitaire) à dualité de Van den Bergh et dont le bimodule dualisant est libre (de rang 1) comme module à gauche et comme module à droite. Le choix d'un générateur libre comme module à gauche permet de décrire la structure de module à droite à l'aide d'un automorphisme (dit <>) de l'algèbre. Les algèbres CY tordues ont été introduites par Reyes, Rogalski et Zhang en 2014, mais de nombreux exemples ont été étudiés auparavant. Ainsi, parmi les algèbres graduées et connexes, ce sont précisément les algèbres d'Artin-Shelter régulières. De même, Yekutieli a démontré en 2000 que les algèbres enveloppantes des algèbres de Lie de dimension finie en font partie. L'exposé fera un survol des algèbres CY tordues. Il sera en particulier question de leurs propriétés homologiques, de leurs usages (notament en géométrie non commutative, au sens d'Artin et Zhang), et des méthodes connues pour en construire et calculer leur automorphisme de Nakayama.
+ Laurent DEMONET Treillis des classes de torsions 15/05/2017 14:00 001
[Collaboration avec Osamu Iyama, Nathan Reading, Idun Reiten et Hugh Thomas] Soit $A$ une algèbre de dimension finie sur un corps $k$. Rappelons qu'une classe de torsion $\mathcal{T}$ dans la catégorie $\mathop{\mathsf{mod}} A$ des $A$-modules de dimension finie est une sous catégorie pleine, stable par extensions et par quotients. Nous supposons que $\mathop{\mathsf{mod}} A$ contient un nombre fini de classes de torsions. Dans ce cas, l'ensemble des classes de torsion ordonné par l'inclusion forme un treillis $\mathop{\mathsf{tors}} A$. Nous étudions les quotients de $\mathop{\mathsf{tors}} A$ en en donnant une description algébrique. En particulier, nous décrivons de façon algébrique la relation de \textit{forçage} sur les flèches du carquois de Hasse de $\mathop{\mathsf{tors}} A$. Nous déduisons des résultats combinatoires importants sur $\mathop{\mathsf{tors}} A$, en particulier que ce treillis est un treillis \textit{uniforme pour ses congruences}. Supposons maintenant que $B$ est un quotient de $A$. Il est immédiat que $\mathop{\mathsf{tors}} B$ est un quotient de $\mathop{\mathsf{tors}} A$ via $\mathcal{T} \mapsto \mathcal{T} \cap \mathop{\mathsf{mod}} B$. Nous nous intéressons donc à caractériser les quotients $L$ de $\mathop{\mathsf{tors}} A$ qui sont de la forme $\mathop{\mathsf{tors}} B$. Nous donnons plusieurs conditions nécessaires sur $L$ qui deviennent suffisantes quand $A$ est suffisamment simple. C'est en particulier le cas pour les algèbres préprojectives de type $A_n$ ou les algèbres héréditaires de type fini. Finalement, nous appliquons nos résultats aux algèbres préprojectives, retrouvant des preuves complètement algébriques de résultats sur les treillis cambriens.
+ Alberto MINGUEZ Autour des induites paraboliques sur un corps local non-archimédien 27/03/2017 14:00 001
Soit $F$ un corps local non-archimédien et $\pi$ une représentation lisse irréductible de $GL(n,F)$, $n\geq 1$. Dans la théorie des représentations de groupes $p$-adiques, il est intéressant de connaître si, pour toute représentation irréductible $\pi'$ de $GL(n',F)$, $n'\geq 1$, la représentation (induite parabolique) $\pi \times \pi'$ de $GL(n+n',F)$ admet une unique sous-représentation irréductible. Cette question a des applications par exemple à la correspondance thêta locale ou encore à la classification des représentations irréductibles unitaires du groupe $GL(n,F)$ et de ses formes intérieures. Or cette propriété est équivalente au fait que $\pi$ soit de carré irréductible, c'est-à-dire $\pi \times \pi$ soit irréductible, ce qui est l'analogue $p$-adique de la notion de ``représentation réelle''. Dans un travail en collaboration avec Erez Lapid nous donnons un critère géométrique nécessaire et suffisant pour qu'une représentation ``régulière'' de $GL(n,F)$ soit de carré irréductible (une représentation est régulière si elle est attachée à un multisegment dont ses segments ont des débuts, et aussi des fins, distincts).
+ Toby STAFFORD Noncommutative rational surfaces 20/03/2017 14:00 001
One of the major open problems in non-commutative algebraic geometry is the classification of non-commutative surfaces (or of connected graded algebras of Gelfand-Kirillov dimension 3). Artin has conjectured that the corresponding division rings are known, with the generic case being the ring of fractions of the so-called Sklyanin algebra. In this talk we will discuss progress in classifying the non commutative surfaces birational to Proj of that algebra. In particular, non-commutative analogues +of blowing up and down are understood, and this has for example been used to determine the subalgebras of the Sklyanin algebra. This talk will survey this subject and show in particular that Van den Bergh's quadric surfaces are minimal models in a very strong sense. This is joint work with Dan Rogalski and Sue Sierra.
+ Pu ZHANG Relations de Baxter asymptotiques des groupes quantiques affines et elliptiques 13/03/2017 14:00 001
Pour les groupes quantiques affines associés aux super algèbres de Lie gl(m|n) et le groupe quantique elliptique de sl(2), nous démontrons des relations de Baxter dans une catégorie BGG de représentations. Ces relations font intervenir des représentations asymptotiques du groupe quantique entier, qui sont des limites d'une famille distinguée de modules irréductibles de dimension finie, les modules de Kirillov-Reshetikhin. Elles donnent lieu aux relations de Baxter pour les matrices de transfert d'un système intégrable quantique. La partie elliptique est un travail en commun avec G. Felder.
+ Lauren WILLIAMS Quiver representations and generalized minors 06/03/2017 14:00 001
The representation theories of both quivers and of Kac-Moody groups are described by certain ternary classifications. On one hand, indecomposable quiver representations are classified as either preprojective, preinjective, or regular according to the action of the Auslander-Reiten translation. On the other, irreducible representations of affine Kac-Moody groups are classified as highest-weight, lowest-weight, or level zero according to their central character (similarly for non-affine types, though the term ``level zero'' is less apt). In both classifications the first two classes are well understood and dual to each other in a suitable sense, while the third is much more mysterious. The theme of the talk is that these two classifications are in fact directly related to one another. We formulate a general conjecture to this effect, which we prove in affine type A and finitely many other types. The conjecture is couched in terms of cluster algebras -- on one hand these are repositories for certain generating functions (called cluster characters) associated to quiver representations, and on the other they are coordinate rings of certain subvarieties of Kac-Moody groups. The conjecture states that the cluster character of a rigid indecomposable quiver representation is a generalized minor of a specific Kac-Moody representation, and that this relationship intertwines the classifications described above. This is joint work with Dylan Rupel and Salvatore Stella.
+ Amnon YEKUTIELI Weak proregularity, weak stability and the noncommutative MGM equivalence 27/02/2017 14:00 001
Let $A$ be a commutative ring, and let $\frak{a}$ be a finitely generated ideal in it. It is known that a necessary and sufficient condition for the derived $\frak{a}$-torsion and the derived $\frak{a}$-adic completion functors to be nicely behaved is the weak proregularity of the ideal $\frak{a}$. In particular, the MGM Equivalence holds under this condition. Because weak proregularity is defined in terms of elements of the ring (specifically, it involves limits of Koszul complexes), it is not suitable for noncommutative ring theory. Consider a torsion class $T$ in the category $M(A)$ of left modules over a ring $A$. We introduce a new condition on $T$: weak stability. Our first main theorem is that when $A$ is commutative, an ideal $\frak{a}$ in $A$ is weakly proregular if and only if the corresponding torsion class $T$ in $M(A)$ is weakly stable. It turns out that when the ring $A$ is noncommutative, one must impose two more conditions on the torsion class $T$: quasi-compactness and finite dimensionality (these are new names for old conditions). We prove that for a torsion class $T$ that is weakly stable, quasi-compact and finite dimensional, the right derived $T$-torsion functor is isomorphic to a left derived tensor functor. This result involves derived categories of bimodules. Some examples will be given. The third main theorem is the Noncommutative MGM Equivalence, under the same assumptions on $T$. Finally, there is a theorem about derived left-sided and right-sided torsion for complexes of bimodules. This last theorem is a generalization of a result of Van den Bergh from 1997, and it corrects an error in a paper of Yekutieli-Zhang from 2003. We expect that the approach outlined in this talk will open up the way to a useful theory of rigid dualizing complexes in the arithmetic noncommutative setting (namely without a base field). The work above is joint with Rishi Vyas.
+ Bertrand RÉMY Génération de groupes profinis de type arithmétique 20/02/2017 14:00 001
Dans cet exposé, il sera question de présentations (engendrement, nombre de relations, taille de présentations) de groupes profinis. Plus précisément, les groupes considérés seront des complétions de groupes arithmétiques. Le but est d’obtenir des résultats de contrôle uniforme de la taille des présentations de ces complétions. Les résultats sont encore partiels et les preuves doivent distinguer caractéristiques nulle et positives, mais les premières uniformités soulèvent des questions intéressantes, impliquant aussi les groupes réductifs dont certains groupes profinis considérés sont les sous-groupes compacts maximaux. C’est un travail commun avec Inna Capdeboscq et Alex Lubotzky.
+ Emmanuel LETELLIER Représentations de carquois sur des algèbres de Frobenius commutatives 30/01/2017 14:00 001
Étant donné une algèbre de Frobenius $R$, nous discuterons du lien entre les représentations d'un carquois sur $R[t]/t^2$ et des représentations de l'algèbre préprojective de ce même carquois sur $R$. Il s'agit d'un travail en cours avec Tamas Hausel et Fernando Rodriguez-Villegas.
+ Anna WEIGANDT Partition identities and quiver representations 23/01/2017 14:00 001
We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A. L. Cauchy's Durfee square identity to multipartitions. We then use this result to give a new proof of M. Reineke's identity in the case of quivers Q of Dynkin type A of arbitrary orientation. Our identity is stated in terms of the lacing diagrams of S. Abeasis - A. Del Fra, which parameterize orbits of the representation space of Q for a fixed dimension vector. This is joint work with R. Rimanyi and A. Yong.
+ Caroline GRUSON Famille des super groupes algébriques orthosymplectiques de type $B(m,n)$ et algèbre de Clifford. 09/01/2017 14:00 001
Soit $F$ la catégorie somme directe des catégories de $B(m,n)$-modules de dimension finie, nous montrerons comment les foncteurs d'induction et de restriction géométriques sur $F$ donnent une catégorification de l'action de l'algèbre de Clifford dans l'espace de Fock des formes semi-infinies.
+ Chun-Ju LAI Affine Hecke algebras and quantum symmetric pairs (projet ERC QAffine) 12/12/2016 14:00 001
In an influential work of Beilinson, Lusztig and MacPherson, they provide a construction for (idempotented) quantum groups of type A together with its canonical basis. While a geometric method via partial flags and dimension counting is applied, it can also be approached using Hecke algebras and combinatorics. In this talk I will focus on the Hecke algebraic approach and present our work on a generalization to affine type C, which produces favorable bases for q-Schur algebras and certain coideal subalgebras of quantum groups of affine type A. We further show that these algebras are examples of quantum symmetric pairs, which are quantization of symmetric pairs consisting of a Lie algebra and its fixed-point subalgebra associated to an involution. This is a joint work (\href{https://arxiv.org/abs/1609.06199}{arXiv:1609.06199}) with Z. Fan, Y. Li, L. Luo, and W. Wang.
+ Matheus BRITO Tensor products of prime representations of quantum affine $sl_{n+1}$ (projet ERC QAffine) 05/12/2016 14:00 001
We study the family of prime representations of quantum affine $sl_{n+1}$ introduced in the work of Hernandez and Leclerc. These are defined by using an $A_n$-quiver; in the case of the sink-source quiver and the monotonic quiver they proved that the associated subcategory of finite–dimensional representations of the quantum affine algebra was a monoidal categorification of a cluster algebra with the prime representations corresponding to cluster variables. In this talk we shall work with an arbitrary quiver and give a necessary and sufficient condition in terms of Drinfeld polynomials for a tensor product of prime representations to be irreducible. We also state precisely the “exchange relations” in the case when a tensor product is reducible; in other words we describe the Jordan–Holder series of the tensor product. As a consequence of our results we write an explicit formula for the character of a prime representation as an alternating linear combination of characters of the local Weyl modules for quantum affine algebras. The talk is based on a joint work with Vyjayanthi Chari
+ Ruari WALKER Morita Equivalences Between KLR Algebras and VV Algebras (projet ERC QAffine) 28/11/2016 14:00 001
A family of graded algebras have been introduced by Khovanov, Lauda and independently by Rouquier, the representation theory of which is closely related to that of the affine Hecke algebras of type A. They are often called KLR algebras, or quiver Hecke algebras, and have been the subject of intense study in past 10 years or so. More recently, Varagnolo and Vasserot have defined a new family of graded algebras whose representation theory is related to the representation theory of the affine Hecke algebras of type B. These algebras can be thought of as type B analogues of KLR algebras in some sense. During this talk I plan to explain this in a little more detail by showing how KLR algebras relate to VV algebras and by comparing their module categories via Morita equivalence. From these equivalences we can deduce properties such as affine cellularity and affine quasiheredity of certain classes of VV algebras.
+ Davide MASOERO Algebraic aspects of the ODE/IM correspondence (projet ERC QAffine) 14/11/2016 14:00 001
The ODE/IM correspondence is a conjectural and surprising link between nonlocal observable of integrable quantum field theories and monodromy data of linear analytic ODEs. In this talk $g$ is a simple Lie algebra over the complex field. Given a pair (L,w) where L is a $^{L} g^{(1)}$-affine oper (of a particular type) and w an element of the Weyl group of g, we construct a solution of the nested Bethe Ansatz equations of the Quantum g-KdV model. We will briefly introduce the physical origin and the main contributions to the ODE/IM correspondence. The talk is based on a joint work with A. Raimondo and D. Valeri.
+ Roland BERGER Calcul de Koszul 07/11/2016 14:00 001
Il s'agit d'un travail en collaboration avec Andrea Solotar et Thierry Lambre (\href{http://arxiv.org/abs/1512.00183}{arXiv1512.00183}). Nous présentons un calcul, dit de Koszul, adapté aux algèbres quadratiques homogènes A. Ce calcul est organisé suivant une homologie et une cohomologie de Koszul munies de cup et cap produits. Si l'algèbre A est Koszul, le calcul de Koszul est isomorphe au calcul de Hochschild, mais il ne l'est pas sur un exemple de A non Koszul explicite. Nous donnerons les principales propriétés du calcul de Koszul en comparaison avec le calcul de Tamarkin-Tsygan. Nous appliquerons ce calcul à la dualité de Koszul en montrant qu'il y a un isomorphisme entre l'algèbre de cohomologie de A et l'algèbre de cohomologie modifiée de sa duale, valable pour toute algèbre quadratique A, Koszul ou non. Cet isomorphisme est complété en homologie par un isomorphisme de bimodules.
+ Eric HOFFBECK Utilisation de catégories supérieures pour les résolutions d'algèbres 30/05/2016 14:00 001
Des propriétés homologiques des monoïdes peuvent être prouvées grâce aux polygraphes (des catégories supérieures, construites inductivement, dont le but est d’encoder la géométrie des relations d’un monoïde, des relations entre les relations, etc). Dans cet exposé, j’exposerai une généralisation de cette notion : les polygraphes linéaires, servant à étudier l’homologie des algèbres associatives. À partir d’une algèbre définie par générateurs et relations, on définit la notion de présentation convergente de cette algèbre, et on construit un polygraphe linéaire associé. On peut en déduire une résolution (explicite) de l’algèbre, permettant de faire des calculs d’homologie. Travail en commun avec Yves Guiraud et Philippe Malbos.
+ Naihong HU Loewy Filtration and Quantum de Rham Cohomology 23/05/2016 14:00 001
This talk is about : (1) the indecomposable submodule structures of quantum divided power algebra $\mathcal{A}_q(n)$ introduced in my earlier work (2000) and its truncated objects $\mathcal{A}_q(n, m)$, where an ``intertwinedly-lifting`` method is established to prove the indecomposability of a module when its socle is non-simple. (2) The Loewy filtrations are described for all homogeneous subspaces $\mathcal{A}^{(s)}_q(n)$ or $\mathcal{A}_q^{(s)}(n, m)$, the Loewy layers and dimensions are determined. The rigidity of these indecomposable modules is proved. An interesting combinatorial identity is derived from our realization model for a class of indecomposable $\mathfrak{u}_q(\mathfrak{sl}_n)$-modules. (3) Meanwhile, the quantum Grassmann algebra $\Omega_q(n)$ over $\mathcal{A}_q(n)$ is defined and constructed, together with the quantum de Rham complex $(\Omega_q(n), d^\bullet)$ via defining the appropriate $q$-differentials, and its subcomplex $(\Omega_q(n, m), d^\bullet)$. For the latter, the corresponding quantum de Rham cohomology modules are decomposed into the direct sum of some sign-trivial modules. This is a joint work with H.X. Gu.
+ Nicolai RESHETIKHIN On solutions to the Yang-Baxter equation related to quantum groups at roots of unity 02/05/2016 14:00 001
+ Martina LANINI Phénomènes périodiques dans la théorie des représentations et graphes moment (projet ERC QAffine) 18/04/2016 14:00 001
Des phénomènes périodiques apparaissent — ou devraient apparaître — dans la théorie des représentations des groupes quantiques en une racine de l'unité, des algèbre de Lie en caractéristique positive, et des algèbre de Kac-Moody affines au niveau critique. Dans une série de travaux en collaboration avec Peter Fiebig, nous définissons et étudions la catégorie des faisceaux cofiltrés sur un graphe de moment affine et montrons qu'elle présente ces mêmes phénomènes de périodicité. Dans mon exposé je vais décrire notre construction et ses applications dans la théorie des représentations des algèbre de Lie en caractéristique positive. (Travaux en commun avec Peter Fiebig.)
+ Ghislain FOURIER PBW filtration, birational sequences, and toric degenerations (projet ERC QAffine) 11/04/2016 14:00 001
The PBW filtration and degeneration for a semi-simple complex Lie algebra provides a fruitful bridge from Lie theory to commutative algebra. We will be focussing on $sl_n$ and recalling the degenerate flag variety, a flat degeneration of the classical flag variety. I'll introduce monomial bases for the PBW degenerate simple $sl_n$-modules and describe the associated flat toric degeneration of the flag variety (this is joint work with E. Feigin and P. Littelmann). In order to set this in context with previously known toric degenerations (due to Caldero, Littelmann, Alexeev-Brion et al), I'll introduce ''birational sequences'', which are in some sense factorizations of a maximal unipotent subgroup of $SL_n$. This provides a framework of toric degenerations that covers for all types the construction of string polytopes, Lusztig polytopes and many more (the latter is joint work with X. Fang and P. Littelmann).
+ Lucy MOSER-JAUSLIN Dérivations localement nilpotentes sur des anneaux gradués 21/03/2016 14:00 001
Dans le développement de la géométrie algébrique affine, l'étude des dérivations localement nilpotentes a joué un rôle important depuis les travaux de L. Makar-Limanov il y a une vingtaine d'années. Elles ont été utilisées pour distinguer différentes variétés affines, ainsi que pour déterminer les groupes d'automorphismes de certaines variétés rationnelles. Le cas des dérivations qui sont homogènes par rapport à une $\mathbb{Z}$-graduation est particulièrement important. Dans cet exposé je vais donner une introduction à cette théorie, et montrer comment on peut la généraliser aux dérivations qui sont homogènes par rapport aux graduations d'autres groupes abéliens. Ce travail est une collaboration avec D. Daigle et G. Freudenburg.
+ Matthew O'DELL Weyl modules for equivariant map algebras with non-free action 14/03/2016 14:00 001
We discuss a family of equivariant map algebras with non-free action. These equivariant map algebras contain, as special cases, all parabolic subalgebras of affine Lie algebras. We compare properties of Weyl modules for these equivariant map algebras to the Weyl modules introduced by Chari and Pressley in 2001.
+ Christian BLANCHET sl(2) quantique déroulé et TQFTs non semisimples 15/02/2016 14:00 001
Les invariants quantiques des entrelacs et des variétés de dimension 3 dits de Witten-Reshetikin-Turaev sont obtenus à partir des représentations du groupe quantique sl(2) aux racines de l'unité. Il existe plusieurs versions de ce groupe quantique , celle qui est utilisé pour les invariants WRT est le petit groupe quantique et plus précisément sa semisimplification. Le groupe sl(2) quantique déroulé est une extension du groupe quantique restreint qui permet de construire une catégorie enrubannée dans laquelle les modules simples sont indexés par des poids complexes. Nous définirons cette catégorie et décrirons ses modules projectifs indécomposables. Costantino, Geer et Patureau ont défini pour chaque entier $p>1$, non congru à 0 modulo 4, des invariants en dimension 3 basée sur ce groupe quantique déroulé. Nous présenterons les TQFTs, non semisimples, qui étendent ces invariants et décrirons algébriquement les espaces vectoriels gradués obtenus, ainsi que l'action des Mapping Class Groups. Travail en commun avec François Costantino, Nathan Geer et Bertrand Patureau.
+ Philip BOALCH Variétés symplectiques non-perturbatives et algèbres non-commutatives 08/02/2016 14:00 001
La correspondance de Riemann-Hilbert (sauvage) sur les courbes peut être vue comme une machine qui prend comme input une variété symplectique/Poisson ``additive'' et donne en retour une variété symplectique/Poisson ``multiplicative''. Depuis 2001 on a compris que cette machine donne le groupe de Poisson-Lie dual $G^*$ (la variété de Poisson non-linéaire au dessous du groupe quantique de Drinfeld-Jimbo) quand l'input est le variété de Poisson linéaire $Lie(G)^*$. Dans cet exposé je vais décrire quelques nouveaux exemples plus compliqués. Par exemple en 2008 (\href{http://arxiv.org/abs/0806.1050}{arXiv:0806.1050}) on a compris qu'une grande classe de variétés de carquois de Nakajima peut être prise comme input (avec des carquois loins d'être affines en général). Si on regarde leurs versions multiplicatives (\href{http://arxiv.org/abs/1307.1033}{arXiv:1307.1033}) on voit une généralisation de la théorie des variétés de carquois multiplicatives et ensuite de nouvelles algèbres noncommutatives (``fission algebras'') qui generalisent les algèbres preprojectives multiplicatives déformées de Crawley-Boevey et Shaw (qui contiennent notamment les DAHAs generalisées d'Etingof-Oblomkov-Rains). Une grande partie de ce travail est l'extension (commencée en 2002, \href{http://arxiv.org/abs/math/0203161}{arXiv:math/0203161}) de la théorie de géométrie Hamiltonienne multiplicative (d'Alekseev-Malkin-Meinrenken) pour encadrer cette nouvelle théorie. Par exemple dans le cas d'un triangle ($A_2$ affine) ou d'une arrête double ($A_1$ affine) on obtient de nouvelles algèbres non-commutatives.
+ Amnon YEKUTIELI Derived Categories of Bimodules 25/01/2016 14:00 001
Homological algebra plays a major role in noncommutative ring theory. One important homological construct related to a noncommutative ring $A$ is the dualizing complex, which is a special kind of complex of $A$-bimodules. When $A$ is a ring containing a central field $K$, this concept is well-understood now. However, little is known about dualizing complexes when the ring $A$ does not contain a central field (I shall refer to this as the noncommutative arithmetic setting). The main technical issue is finding the correct derived category of $A$-bimodules. In this talk I will propose a promising definition of the derived category of $A$-bimodules in the noncommutative arithmetic setting. Here $A$ is a (possibly) noncommutative ring, central over a commutative base ring $K$ (e.g. $K=Z$). The idea is to resolve $A$: we choose a DG (differential graded) ring $A'$, central and flat over $K$, with a DG ring quasi-isomorphism $A'\to A$. Such resolutions exist. The enveloping DG ring $A'^{\text{en}}$ is the tensor product over $K$ of $A'$ and its opposite. Our candidate for the ``derived category of $A$-bimodules'' is the category $D(A'^{\text{en}})$, the derived category of DG $A'^{\text{en}}$-modules. A recent theorem says that the category $D(A'^{\text{en}})$ is independent of the resolution $A'$, up to a canonical equivalence. This justifies our definition. Working within $D(A'^{\text{en}})$, it is not hard to define dualizing complexes over $A$, and to prove all their expected properties (like when $K$ is a field). We can also talk about rigid dualizing complexes in the noncommutative arithmetic setting. What is noticeably missing is a result about existence of rigid dualizing complexes. When the $K$ is a field, Van den Bergh had discovered a powerful existence result for rigid dualizing complexes. We are now trying to extend Van den Bergh's method to the noncommutative arithmetic setting. This is work in progress, joint with Rishi Vyas. In this talk I will explain, in broad strokes, what are DG rings, DG modules, and the associated derived categories and derived functors. Also, I will try to go into the details of a few results and examples, to give the flavor of this material.
+ Sarah SCHEROTZKE Variétés de carquois géneralisées et catégories d'orbites (projet ERC QAffine) 18/01/2016 14:00 001
+ Polyxeni LAMPROU Une nouvelle interprétation des nombres de Catalan 11/01/2016 14:00 001
En étudiant le cristal $B(\infty)$ de Kashiwara, Joseph a introduit des ensembles $H^t$, $t\in \mathbb{N}$ de fonctions données par des classes d'équivalence de partitions non-ordonnées satisfaisant certaines conditions limites. Nous avons montré que le cardinal de $H^t$ est le $t$-ième nombre de Catalan $\mathcal{C}_t$. C'est une nouvelle réalisation des nombres de Catalan qui admet de plus quelques propriétés remarquables. On associe à $H^t$ un graphe numéroté $\mathscr{G}_t$ qui se décompose canoniquement en une réunion de $(t-1)!$ sous-graphes chacun ayant $2^{t-1}$ sommets. On peut décrire ces sous-graphes comme hypercubes numérotés dans $\mathbb{R}^{t-1}$ dont quelques arêtes sont effacées. On montre que le nombre d'hypercubes distincts obtenus de cette façon est encore un nombre de Catalan, à savoir $\mathcal{C}_{t-1}$. Ils définissent des fonctions qui dépendent d'un ensemble de coefficients non-négatifs. Quand ces coefficients sont non-nuls et deux-à-deux distincts, les sommets des hypercubes décrivent des fonctions distinctes. De plus, cette propriété est encore vraie si on efface certaines arêtes et si on identifie certains sommets. En particulier, quand ces coefficients sont tous égaux et non-nuls, on montre que tout hypercube dégénère en un simplex, donnant précisément $t$ fonctions distinctes, qui sont par exemple les fonctions nécessaires pour la description de $B(\infty)$ en type $A$. Ce travail est joint avec A. Joseph (\href{http://arxiv.org/abs/1512.00406}{arXiv:1512.00406}).
+ Fan QIN Algèbres amassées quantiques, groupes quantiques et catégorification monoïdale (projet ERC QAffine) 14/12/2015 14:00 001
Dans cet exposé, j'introduirai les conjectures sur la catégorification monoïdale d'une algèbre amassée. Ensuite, je construirai une base triangulaire d'une algèbre amassée, qui admet une paramétrisation par des points tropicaux. Cette construction implique la conjecture de catégorification monoïdale de Hernandez-Leclerc et la conjecture de Fock-Goncharov pour les algèbres amassées quantiques qui proviennent des algèbres affines quantiques.
+ Natalia IYUDU Sklyanin algebras via Groebner bases 07/12/2015 14:00 001
We will talk about new techniques in the study of $3$-dimensional Sklyanin algebras $S(p,q)$. These allow to give purely combinatorial proofs of the facts like Koszulity, PBW, polynomial type of the Hilbert series, etc. depending on parameters.
+ Dimitri GOUREVICH Derivatives in noncommutative calculus and deformation property of quantum algebras 16/11/2015 14:00 001
Recently we have introduced partial derivatives on the algebras U(gl(m)). Consequently, we have succeeded in developing a calculus on these enveloping algebras. In this connection the following question arises: how it is possible to define similar operators on other Noncommutative algebras, in particular, those related to quantum R-matrices? I plan to consider deformation property of the corresponding differential algebras. Also, I'll discuss deformation property of an algebra arising from the Jackson derivative.
+ Jacob GREENSTEIN Bases canoniques doubles 02/11/2015 14:00 001
Le but de cet exposé est de définir la base canonique dans l'algèbre enveloppante quantifiée d'une algèbre de Kac-Moody symmétrisable et de décrire ses propriétés, en particulier, par rapport à l'action du groupe de tresses correspondant et sa relation avec le centre du groupe quantique de type fini. (D'après des travaux en commun avec Arkady Berenstein).
+ Tom LENAGAN The usefulness of Cauchon techniques in studying totally nonnegative matrices 12/10/2015 14:00 001
A real matrix is totally nonnegative if each of its minors is nonnegative. Specifying the minors which are zero produces a cell decomposition of totally nonnegative matrices of a given size. The deleting derivations algorithm introduced by Cauchon with great success in studying quantum matrices and other noncommutative algebras can be used to investigate the cell decomposition of totally nonnegative matrices in an efficient manner. In this talk I will describe work of Goodearl, Launois and myself showing how this happens. Also, I will give new proofs of some old results about totally nonnegative matrices by using the Cauchon techniques.
+ Anne MOREAU Idéaux de Joseph et W-algèbres lisses 05/10/2015 14:00 001
Motivés par des travaux récents de Kawasetsu, nous considérons un relèvement des idéaux de Joseph associés aux adhérences d'orbites nilpotentes minimales au cadre des algèbres de Kac-Moody affines, et obtenons de nouveaux exemples d'algèbres vertex affines dont la variété associée est l'adhérence d'une orbite nilpotente minimale. Comme application, nous en déduisons une nouvelle famille de W-algèbres lisses. Il s'agit d'un travail en commun avec Tomoyuki Arakawa.
+ Stéphane LAUNOIS Sur l’équivalence de Dixmier-Moeglin pour les algèbres de Poisson 08/06/2015 14:00 001
En 2002, Brown et Gordon ont posé la question de savoir si les trois ensembles suivants coincident toujours pour les algèbres de Poisson affines : l’ensemble des idéaux Poisson rationnels, l’ensemble des idéaux Poisson primitifs et l’ensemble des idéaux Poisson localement clos. Le but de cet exposé est de répondre à cette question. (Travail en commun avec Jason Bell, Omar Leon Sanchez et Rahim Moosa).
+ Natasha ROZHKOVSKAYA Construction of vertex operators from Jacobi-Trudi identities 01/06/2015 14:00 001
The action of algebra of fermions on the Fock space allows to construct the action on the same space of other interesting algebras, such as Heisenberg algebra, Virasoro algebra and $gl_\infty$. Boson-fermion correspondence allows to identify Fock space with boson space as modules over Heiseinberg algebra, and describes the action of algebra of fermions in terms of vertex operators (generating functions). One can notice that in this construction the crucial role is played by a property that is equivalent to the Jacobi-Trudi identity for symmetric functions. In this talk we will review the classical construction and will discuss, how more general identity can be used to construct the action algebra of fermions. This will be illustrated with examples that naturally appear in representation theory and in generalizations of symmetric functions.
+ Johannes SINGER Shuffle renormalization of (q-)multiple zeta values 18/05/2015 14:00 001
Multiple zeta values (MZVs) are multidimensional generalizations of the Riemann zeta function which are usually studied at positive integers. It is a natural question to ask for MZVs defined for non-positive arguments. In dimension greater than one - in contrast to the case of Riemann zeta function - there are tuples of non-positive integers belonging to the pole set of the meromorphic continuation of MZVs. In the talk we study the Hopf algebra of multiple polylogarithms and the corresponding q-analogue at non-positive arguments which are related to the shuffle product of MZVs. In order to obtain renormalized MZVs for all non-positive arguments we apply the procedure of renormalization introduced by Connes and Kreimer in perturbative quantum field theory. This is a joint work with Kurusch Ebrahimi-Fard and Dominique Manchon.
+ Michaël BULOIS Nappes et induction 13/04/2015 14:00 001
Etant donné un groupe algébrique G agissant sur une variété V, une nappe est une composante irréductible d'un $V_m:=\{x \in V | \dim G.x=m\}$. Le but de cet exposé est de présenter des résultats sur les nappes de l'action adjointe de G, supposé réductif, sur son algèbre de Lie ainsi que des généralisations vers des cas gradués (algèbres de Lie symétriques, theta-représentations). Ce faisant, on est amené à généraliser (et modifier) la notion d'induction d'orbites nilpotentes de Lusztig-Spaltenstein.
+ Micha PEVZNER Opérateurs de brisure de symétrie pour les paires réductives 23/03/2015 14:00 001
Sous certaines conditions les entrelacements qui apparaissent dans les lois de branchement des représentations des groupes de Lie réductifs réels sont réalisés par des opérateurs différentiels. Nous expliquerons leur nature algébrique et géométrique, présenterons une méthode générale de leur construction et esquisserons quelques applications.
+ Alfons OOMS On the polynomiality of the Poisson center and semi-center of a Lie algebra of index at most two 09/03/2015 14:00 !005
Let L be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero and let S(L) be its symmetric algebra, equipped with its natural Poisson structure. L is called coregular if the Poisson center of S(L) is polynomial. We collect some simple criteria in order for this to occur. Examples show that this happens very rarely when the index of L is rather large, compared to the dimension of L. Therefore it seems natural to let the index be at most two. Under this condition any nilpotent Lie algebra is coregular. This result is not true in the solvable case or if the index is equal to three. On the other hand, any nonsolvable Lie algebra of dimension at most eight is coregular. A counterexample is given in dimension nine.
+ Shmuel ZELIKSON Jeux de nombres d'Auslander-Reiten 02/03/2015 14:00 001
Un jeu de nombres (au sens de Mozes) a pour tableau un graphe fini G. Un état de jeu consiste en une valuation des sommets de G par des nombres entiers. Les mouvements de jeu sont entièrement définis à partir de la structure de G. Un tel jeu, avec le diagramme de Dynkin comme tableau a été introduit par Mozes pour modéliser l'orbite sous le groupe de Weyl d'un poids dominant. Soit g une algèbre de Lie simple complexe de type ADE. Nous verrons qu'un jeu de nombres permet d'obtenir les multiplicités de poids d'une représentation simple de dimension finie. Il constitue donc une solution combinatoire pour la formule de caractères de Weyl, à savoir une famille d'objets dont la cardinalité de ceux d'un poids donné, est égale à la multiplicité de l'espace de poids correspondant. Ce jeu se joue sur le carquois d'Auslander-Reiten attaché à une orientation du diagramme de Dynkin de g.
+ Jean-Philippe MICHEL Déterminants sur les algèbres graduées-commutatives 23/02/2015 14:00 001
Cet exposé vise à présenter les rudiments de l'algèbre linéaire, en particulier la notion de déterminant, sur une algèbre graduée-commutative, pour un groupe graduant abélien de type fini et un bi-caractère quelconque. Les exemples de telles algèbres abondent, par ordre de généralité: algèbres des quaternions, de Clifford, de matrices. L'outil fondamental pour cette étude est l'équivalence de catégorie [dûe à Nekludova et Scheunert, '70] entre algèbres graduées-commutatives et algèbres supercommutatives. Lorsque cette équivalence est directement applicable (matrices de degré 0), elle fournit une formule simple et complètement explicite pour le déterminant ainsi qu'une élégante caractérisation (généralisation du theorème de [McDonald '82]). Au contraire, pour les matrices quelconques (correspondant aux endomorphismes internes de modules gradués), l'approche catégorique ne permet plus de construire un déterminant multiplicatif, comme celui bien connu sur les quaternions [Dieudonné '43]. L'exposé sera illustré par quelques exemples. Il repose sur le preprint arXiv:1403.7474, écrit en collaboration avec Tiffany Covolo (Université du Luxembourg).
+ Amaury FRESLON La combinatoire des partitions et la notion de groupe quantique libre 02/02/2015 14:00 001
La combinatoire des partitions d'ensembles finis permet de produire des catégories tensorielles naturellement reliées à la théorie des représentations de certains groupes compacts. Ces constructions admettent des généralisations naturelles qui sont associées à des groupes quantiques compacts au sens de Woronowicz. Après avoir introduit ce cadre général des ``groupes quantiques de partitions'', j'expliquerai comment il permet d'étudier les liens entre différentes notions de liberté pour les groupes quantiques.
+ Lauren WILLIAMS Cluster duality and mirror symmetry for Grassmannians 26/01/2015 14:00 001
We consider the Grassmannian $X=Gr_{n-k,n}$ and its mirror dual Landau-Ginzburg model ($X$-check, $W$), which takes place on a dual Grassmannian. Postnikov's theory of plabic graphs can be used both to parameterize a dense open subset of $X$, and to describe the cluster structure on $X$-check. For each reduced plabic graph $G$ associated to $X$, we describe an associated Newton-Okounkov polytope as a convex hull of certain lattice points. We show that the same polytope, but described in terms of inequalities, can be obtained by ``tropicalizing'' the superpotential $W$, after writing it in terms of the cluster associated to $G$.
+ Alfredo NÁJERA CHÁVEZ Une catégorification des algèbres amassées universelles de type finie. 19/01/2015 14:00 001
Dans cet exposé je présenterai une catégorification des algèbres amassées universelles associées aux carquois de Dynkin. Ces catégories sont définies comme les catégories d’orbites associées aux catégories de Nakajima (dans le sens de Keller et Scherotzke) munies d’un automorphisme distingué. Si le temps le permet, je présenterai des applications aux algèbres amassées.
+ Anne-Sophie GLEITZ Algèbres de lacets quantiques aux racines de l'unité et algèbres amassées généralisées 12/01/2015 14:00 001
L'algèbre de lacets quantique $U_q^{}(L\mathfrak{sl}_2)$ se spécialise à une racine de l'unité $\varepsilon$, pour obtenir l'algèbre $U_\varepsilon^{res}(L\mathfrak{sl}_2)$. Dans l'esprit des travaux de Hernandez et Leclerc sur $U_q^{}(L\mathfrak{g})$ (2013), on démontre que l'anneau de Grothendieck d'une sous-catégorie tensorielle $\mathcal{C}_{\varepsilon^{\mathbb{Z}}}$ des représentations de dimension finie de $U_\varepsilon^{res}(L\mathfrak{sl}_2)$, est isomorphe à une algèbre amassée généralisée $\mathcal{A}_{\ell-1}$ de type $C_{\ell-1}$ (où $\ell$ est l'ordre de $\varepsilon^2$). De plus, l'isomorphisme d'anneaux ainsi construit fait correspondre la base des classes des modules simples à celle des monômes de variables d'amas multipliés par les polynômes de Tchebychev en l'unique coefficient de $\mathcal{A}_{\ell-1}$. En particulier, les variables d'amas sont identifiées aux classes des modules de Kirillov-Reshetikhin qui restent simples après la spécialisation $q=\varepsilon$. Une conjecture est également formulée pour $U_\varepsilon^{res}(L\mathfrak{sl}_3)$ et démontrée dans le cas $\ell=2$, où l'on exhibe une algèbre amassée généralisée de type $G_2$.
+ Patrick LE MEUR La dimension globale forte 15/12/2014 14:00 001
La dimension globale forte a été introduite pour une algèbre $A$ de dimension finie par Ringel: c'est la borne supérieure des longueurs des réolutions projectives des objets indécomposables ces derniers étant pris dans la catégorie homotopique des complexes bornés de $A$-modules projectifs. Happel et Zacharia on démontré que cet invariant, qui est au moins égal à  la dimension globale, est fini précisément pour les algèbres héréditaires par morceaux (\textit{i.e.} dont la catégorie dérivée bornée est équivalente à  celle d'une catégorie abélienne héréditaire). L'exposé présentera diverses interprétations de la dimension globale forte en termes de théorie d'Auslander-Reiten, de mutations basculantes et de sous-catégories abéliennes héréditaires génératrices de la catégorie dérivée bornée. En particulier il expliquera quelques liens entre cet invariant et le nombre de ``morceaux'' d'une algèbre héréditaire par morceaux.
+ A. SOLOTAR Description des algèbres down-up qui sont 3-Calabi-Yau et de celles qui sont monomiales. 08/12/2014 14:00 001
J'utiliserai la résolution des algèbres ``down-up'' obtenue dans ``Projective resolutions of associative algebras and ambiguities'' (\href{http://arxiv.org/abs/1406.2300v2}{arXiv:1406.2300}) pour en étudier les propriétés. Il s'agit d'un travail en collaboration avec Sergio Chouhy.
+ Nicolas JACON Séries de Harish-Chandra pour les groupes unitaires finis et graphes cristallins 24/11/2014 14:00 001
La philosophie d'Harish-Chandra permet d'obtenir une classification des modules simples pour les groupes finis de type Lie en caractéristique non définie. Nous formulons une série de conjectures concernant cette classification dans le cas des groupes unitaires finis. En particulier, nous étudions les liens unissant ce problème avec la théorie des cristaux pour les groupes quantiques en type A affine. C'est un travail commun avec T. Gerber (Aachen) et G.Hiss (Aachen).
+ Maxim NAZAROV Representations of Yangians via Howe duality 17/11/2014 14:00 001
Yangians and their twisted analogues first appeared as basic examples of affine quantum groups and affine symmetric spaces, and found numerous applications as Quantum Integrable Systems. More recently, they made a remarkable appearance in the theory of finite W-algebras. Classification of the irreducible finite-dimensional representations of these Yangians has been known for a long time, but explicit realisations of these representatitions were not known except in special cases. In this talk, it will be explained how to realise all these representations as quotients in tensor products of ``basic'' representations, by using the theory of Mickelsson algebras along with the Howe duality.
+ Sergey MOZGOVOY Commuting matrices and Kac polynomials 03/11/2014 14:00 001
I will discuss the problem of counting pairs of commuting matrices over a finite field. Then I will show how this problem can be generalised to the counting of representations of preprojective algebras associated to quivers and how Donaldson-Thomas invariants and Kac polynomials naturally arise in this context.
+ Yann PALU Pseudo-équivalences de Morita provenant d'objets rigides. 13/10/2014 14:00 001
Le basculement (tilting) est un outil permettant de décrire les équivalences dérivées entre algèbres de dimension finie. D'un point-de-vue combinatoire, les modules basculants souffrent de certains défauts : ils ne peuvent pas toujours être ``mutés''. Une version plus récente de cette théorie, l'amas-basculement (cluster tilting), a été introduite par Buan-Marsh-Reineke-Reiten-Todorov en vue de catégorifier les algèbres amassées de Fomin-Zelevinsky. Les objets amas-basculants ont une bonne théorie de la mutation. De plus, les algèbres d'endomorphismes de deux objets amas-basculants liés par une mutation ne sont pas très loin d'être équivalentes au sens de Morita. L'objectif de cet exposé est de présenter une généralisation de ce dernier phénomène, s'appliquant aux algèbres d'endomorphismes d'objets rigides.
+ Stéphane GAUSSENT Sur les présentations cohérentes des monoïdes d'Artin 06/10/2014 14:00 001
Les monoïdes d'Artin sont les généralisations à tout groupe de Coxeter du monoïde des tresses pour le groupe symétrique. En utilisant des méthodes de réécriture de dimension supérieure, nous calculons diverses présentations cohérentes de ces monoïdes, c'est-à-dire les générateurs, les relations et les relations entre les relations. Nous montrons que dans le cas de la présentation d'Artin, ces relations entre les relations sont données par des 3-cellules dites de Tits-Zamolodchikov. C'est un travail en commun avec \href{http://www.pps.univ-paris-diderot.fr/~guiraud/}{Yves Guiraud} et \href{http://math.univ-lyon1.fr/homes-www/malbos/}{Philippe Malbos}.
+ Sachin GAUTAM Towards a Kohno-Drinfeld theorem for qKZ equations 02/06/2014 14:00 001
+ Valerio TOLEDANO LAREDO Connexions elliptiques associées aux systèmes de racines 26/05/2014 14:00 001
+ Anthony JOSEPH Relative Yangians of Weyl type 19/05/2014 14:00 001
+ Olivier DUDAS Modules projectifs dans la cohomologie des variétés de Deligne-Lusztig 12/05/2014 14:00 001
La cohomologie à coefficients dans un corps de caractéristique positive des variétés de Deligne-Lusztig produit des représentations modulaires des groupes réductifs finis. Dans cet exposé je donnerai quelques propriétés et conjectures (en commun avec G. Malle) permettant d'identifier les représentations qui apparaissent. J'illustrerai ces phénomènes sur de petits exemples comme les groupes $SU_4(q)$ ou $G_2(q)$ où déjà les méthodes algébriques se sont révélées insuffisantes.
+ Ilaria DAMIANI Algèbres quantiques affines: sur l'isomorphisme entre la présentation de Drinfeld-Jimbo et la réalisation de Drinfeld. 14/04/2014 14:00 001
Dans cet exposé on rappelle l'homomorphisme (surjectif) de la réalisation de Drinfeld vers la présentation de Drinfeld-Jimbo des algèbres quantiques affines et on montre l'injectivité. La preuve est basée sur la spécialisation à 1, grâce à l'étude de la décomposition triangulaire de Drinfeld, du cas classique (q=1) et des symétries de ces algèbres. Comme conséquence on obtient une présentation des algèbres de Kac-Moody affines en termes de générateurs de Drinfeld.
+ Susan SIERRA Dynamics of automorphisms, noetherian rings, and the Virasoro algebra 07/04/2014 14:00 001
This talk links algebraic geometry, noncommutative ring theory, and the Virasoro Lie algebra, known for its importance in conformal field theory. We begin with a question in ring theory. Let X be a projective surface with an automorphism a, and consider the skew polynomial extension k(X)[t; a]. Which finitely generated graded subalgebras are noetherian? It turns out that, morally, if a has dense orbits on X there are many noetherian subalgebras, and if not there are few. In the first part of the talk we explain this. In the second, we show how this leads to a proof that the enveloping algebra of the Virasoro algebra is not noetherian.
+ Robin ZEGERS q,t-caractères et structure des espaces de l-poids dans les modules standards des algèbres quantiques affines 31/03/2014 14:00 001
Je présenterai une preuve d'une conjecture de Nakajima établissant une formule pour les q,t-caractères des modules standards sur les algèbres quantiques affines simplement lacées. Cette formule relie la filtration de Jordan naturelle des espaces de l-poids de ces modules aux polynômes de Poincaré de certaines fibres dans les variétés de carquois graduées correspondantes; polynômes en terme desquels les q,t-caractères ont reçu leur définition géométrique initiale. Une preuve algébrique sera présentée en rang 1. En rang supérieur, la preuve est essentiellement géométrique et repose sur le théorème de Lefschetz difficile pour une famille de faisceaux amples intervenant dans la réalisation K-théorique de la sous-algèbre de Heisenberg filtrante.
+ Simon RICHE Faisceaux pervers à coefficients modulaires sur G/B 17/03/2014 14:00 001
Dans cet exposé je présenterai des travaux avec Pramod Achar qui visent à généraliser au cas des coefficients modulaires certains résultats bien connus sur la catégorie des faisceaux pervers à coefficients complexes sur une variété de drapeaux G/B (dualité de Koszul, dualité de Ringel, combinatoire de Kazhdan-Lusztig). La principale différence apparait dans le fait que dans de nombreux énoncés il faut remplacer les complexes de cohomologie d'intersection par les ``faisceaux parités'' de Juteau-Mautner-Williamson. Les motivations pour étudier ces questions viennent de la théorie des représentations (et notamment de la conjecture de Lusztig sur les représentations modulaires des groupes algébriques réductifs).
+ Amnon YEKUTIELI Duality and Tilting for Commutative DG Rings 24/02/2014 14:00 001
We study super-commutative nonpositive DG rings. An example is the Koszul complex associated to a sequence of elements in a commutative ring. More generally such DG rings arise as semi-free resolutions of rings. They are also the affine DG schemes in derived algebraic geometry. The theme of this talk is that in many ways a DG ring $A$ resembles an infinitesimal extension, in the category of rings, of the ring $H^0(A)$. I first discuss localization of DG rings on $Spec(H^0(A))$ and the cohomological noetherian property. Then I introduce perfect, tilting and dualizing DG $A$-modules. Existence of dualizing DG modules is proved under quite general assumptions. The derived Picard group $DPic(A)$ of $A$, whose objects are the tilting DG modules, classifies dualizing DG modules. It turns out that $DPic(A)$ is canonically isomorphic to $DPic(H^0(A))$, and that latter group is known by earlier work. A consequence is that $A$ and $H^0(A)$ have the same (isomorphism classes of) dualizing DG modules.
+ Fan QIN Variétés carquois et groupes quantiques 10/02/2014 14:00 001
Dans cet exposé, je donnerai une famille de variétés carquois cycliques. Cela permettra une approche géométrique aux groupes quantiques de type ADE. Comme un sous-produit, on obtiendra une base globale qui contient la base canonicale duale.
+ Eric VASSEROT Actions catégoriques et algèbres de Hecke doublement affines rationnelles 27/01/2014 14:00 001
+ Florent SCHAFFHAUSER La correspondance de Narasimhan et Seshadri pour les fibrés réels et quaternioniques 20/01/2014 14:00 001
Ce travail comporte deux parties. Dans une première partie, nous expliquons comment construire, à l'aide de notions classiques de théorie de jauge, des espaces de modules pour les fibrés vectoriels algébriques sur une courbe définie sur le corps des réels. Les techniques utilisées permettent de construire également des espaces de modules pour les fibrés vectoriels quaternioniques, qui apparaissent de manière naturelle lorsque l'on s'intéresse au problème des modules pour les fibrés réels. Dans une seconde partie, nous étudions ce qu'il advient dans ce contexte de la correspondance de Narasimhan et Seshadri et nous en déduisons une démonstration simple du fait que les espaces de modules construits au point précédent sont non vides lorsque la courbe de base possède des points réels. Les variétés de représentations de groupes fondamentaux obtenues dans la deuxième partie présentent de fortes analogies avec l'espace de Teichmüller d'une courbe algébrique réelle.
+ Natalia IYUDU The proof of the Kontsevich conjecture on noncommutative birational transformations 13/01/2014 14:00 001
I will talk about our recent proof (arXiv1305.1965) of the Kontsevich conjecture dated back at 1996, and mentioned at the 2011 Arbeitstagung talk on 'Noncommutative identities' (arXiv1109.2469). This conjecture says that certain transformations given by matrices over free noncommutative algebra with inverses are periodic, on the level of orbits of the left/right diagonal action. Namely, let $M_{ij}, 1\leq i,j \leq 3$ be a matrix, whose entries are independent noncommutative variables. Let us consider three birational involutions: $\quad I_1: M \to M^{-1}\quad$ $I_2: M_{ij} \to (M_{ij})^{-1}, \forall i,j \quad$ $I_3: M \to M^t\quad$ Then the composition $\Phi=I_1 \circ I_2 \circ I_3 $ has order three.
+ Dimitri GUREVICH Quantization of Weyl algebras 16/12/2013 14:00 001
Given a commutative associative algebra A=Sym(V), where V is a vector space,  the corresponding Weyl algebra W(A) is  generated by A and partial derivatives in generators of A.  In my talk I'll discuss how it is possible to generalize this notion (as well as that of the corresponding differential algebra) to some Noncommutative algebras. Namely, I'll consider two cases: 1.  A=U(gl(n)) and 2.  A is a braided algebra, i.e. that arising from a braiding (a solution to the Quantum Yang-Baxter Equation). Applications to Mathematical Physics will be given.
+ Alexey SEVASTYANOV Strictly transversal slices in algebraic groups and Lusztig's partition 09/12/2013 14:00 001
In this talk I shall show that for every conjugacy class in a complex semi-simple algebraic group G there is a strictly transversal slice Sg, i.e. an algebraic subvariety of G which intersects the class at an element g of G, and the codimension of the slice is equal to the dimension of the conjugacy class. The most general construction of slices transversal to conjugacy classes in algebraic groups was suggested by me in 2008. This construction generalizes the Steinberg cross-section to the set of regular conjugacy classes in algebraic groups. Recently Lusztig introduced a partition of G with a finite number of strata. It turns out that it suffices to verify the condition of strict transversality of the slices Sg for the conjugacy class Og of a single representative g in each stratum of Lusztig's partition. The finite family of the conjugacy classes Og contains all unipotent classes and possibly a few conjugacy classes of exceptional elements. In case of exceptional Lie groups verification of the strict transversality condition is based on a computer calculation (as well as the definition of Lusztig's partition). The construction of the slices Sg is used in the proof of De Concini-Kac-Procesi conjecture the algebraic part of which will be discussed in my talk on December 16.
+ Yuriy DROZD Tilting and resolutions for singular curves 18/11/2013 14:00 001
+ Pierre-Guy PLAMONDON Mutations et graphes d'échange 04/11/2013 14:00 001
La mutation est un processus qui a été défini par Fomin et Zelevinsky dans la théorie des algèbres amassées. Ce processus permet de construire, au sein d'une telle algèbre, un ensemble de générateurs dont chaque élément est un polynôme de Laurent en un nombre fini de variables fixées au départ. Dans cet exposé, nous aborderons un processus similaire de mutation qui apparaît dans certaines catégories triangulées. Nous verrons que cette mutation et celle des algèbres amassées sont étroitement liées, et que le point de vue catégorique permet de répondre à des questions posées par Fomin et Zelevinsky sur des propriétés combinatoires de la mutation. (Ceci est un travail commun avec G. Cerulli Irelli, B. Keller et D. Labardini-Fragoso).
+ Luca MOCI Matroids over a ring: motivations, examples, applications. 14/10/2013 14:00 001
Several objects can be associated to a list of vectors with integer coordinates: among others, a family of tori called toric arrangement, a convex polytope called zonotope, a function called vector partition function. These objects and their relations have been described in a recent book by De Concini and Procesi. The linear algebra of the list of vectors is retained by the combinatorial notion of a matroid; but several properties of the objects above depend also on the arithmetics of the list. This can be encoded by the notion of a ``matroid over Z''. Similarly, applications to tropical geometry suggest the introduction of matroids over a discrete valuation ring. Motivated by the examples above, we introduce the more general notion of a ``matroid over a commutative ring R''. Such a matroid arises for example from a list of elements in a R-module. When R is a Dedekind domain, we can extend the usual properties and operations holding for matroids (e.g., duality). We can also compute the Tutte-Grothendieck ring of matroids over R; the class of a matroid in such a ring specializes to several invariants, such as the Tutte polynomial and the Tutte quasipolynomial. We will also outline other possible applications and open problems. (Joint work with Alex Fink).
+ Sachin GAUTAM Tensor isomorphism between Yangians and quantum loop algebras 10/06/2013 14:00 001
The Yangian and the quantum loop algebra of a simple Lie algebra arise naturally in the study of the rational and trigonometric solutions of the Yang--Baxter equation, respectively. The aim of this talk is to establish an explicit relation between these Hopf algebras. More precisely, we will show that a certain subcategory of finite--dimensional representations of the Yangian is isomorphic, as a tensor category, to the category of finite--dimensional representations of the quantum loop algebra. The isomorphism between these two categories is governed by the monodromy of an abelian difference equation. Moreover, the twist relating the tensor products is a solution of an abelian version of the qKZ equations of Frenkel and Reshetikhin. These results are part of an ongoing project, joint with V. Toledano Laredo.
+ Miranda CHENG Umbral Moonshine and Niemeier Lattices 03/06/2013 14:00 001
In this talk I will discuss how a new type of moonshine – the umbral moonshine – arises from the 24 even unimodular lattices in 24 dimensions. In more details, for each of the 24 Niemeier lattices we pose an umbral moonshine conjecture identifying a specific set of mock modular forms and the graded characters of a certain natural module of a finite group arising from the automorphism of the Niemeier lattice. The construction of the set of mock modular forms relies on an ADE classification of mock modular forms of a certain type, analogous to the ADE classification of modular invariant combinations of characters of $A_1^{(1)}$ affine Kac-Moody algebra by Cappelli–Itzykson–Zuber, as well as the relation between mock modular forms and meromorphic Jacobi forms studied by S. Zwegers and Dabholkar–Murthy–Zagier. If time permits I will discuss certain mysterious group theoretic properties of this moonshine, the possible relations to certain generalised Kac-Moody algebras, or/and Gromov–Witten theory of certain Calabi–Yau three-folds. This talk is mainly based on joint work with J Duncan and J Harvey.
+ Ivan MARIN Sur la conjecture de liberté des algèbres de Hecke cyclotomiques 22/04/2013 14:00 001
Depuis les années 90 il existe un faisceau de conjectures concernant les généralisations des algèbres de Iwahori-Hecke à des algèbres similairement associées à des groupes de réflexions complexes finis, en lieu et place des habituels groupes de Weyl. Ces conjectures, apparues originellement dans le contexte des représentations des groupes réductifs finis, sont désormais admises dans un nombre de plus en plus important de travaux, qui impliquent soit ces algèbres de Hecke cyclotomiques elles-mêmes, soit des objets reliés comme les algèbres de Cherednik. La première d'entre elles concerne la structure de module de ces algèbres, conjecturées être libres de rang fini sur un anneau convenable. Dans cet exposé, je présenterai et ferai le point sur cette conjecture, incluant des progrès récents sur le sujet.
+ Wendy LOWEN Hochschild cohomology with support and the Grothendieck construction 15/04/2013 14:00 001
In this talk we explain how the functoriality properties of Hochschild cohomology are essentially determined by an underlying level of ``grading categories''. We describe some techniques for deconstructing Hochschild cohomology, based upon sheaf properties and arrow categories, and we relate this to a generalized Grothendieck construction.
+ Mathieu MANSUY Modules extrémaux pour les algèbres toroïdales quantiques 08/04/2013 14:00 001
Kashiwara a défini une classe de représentations intégrables des algèbres affines quantiques appelées représentations extrémales. Il s'agit de représentations, avec une base cristalline, paramétrées par le réseau des poids intégraux. Ces représentations ont une importance particulière car, pour certains poids, elles ont des quotients de dimension finie. Dans cet exposé, nous présentons une généralisation de ces représentations pour l'algèbre toroïdale quantique, affinisation de l'algèbre affine quantique. En particulier nous obtenons là aussi des représentations de dimension finie, aux racines de l'unité.
+ Nicolas RESSAYRE Distributions sur les espaces homogènes et applications 25/03/2013 14:00 001
En 2006, Belkale-Kumar ont défini un nouveau produit sur le groupe de cohomologie $H^*(G/P,R)$ d’un espace homogène rationnel complexe $G=P$. Ce produit permet d’apporter une réponse élégante au problème de Horn pour l’algèbre de Lie d’une forme compacte du groupe complexe $G$. Alors que la construction de Belkale-Kumar utilise la base de Schubert, nous donnerons ici une construction géométrique de ce produit, à l’aide de distributions sur $G=P$. Nous donnerons aussi une application de ces distributions à la géométrie des variétés de Schubert.
+ Ruslan MAKSIMAU Bases canoniques, algèbres KLR, faisceaux de parité. 11/03/2013 14:00 001
On construit une base de la partie positive d'un groupe quantique de type fini en termes des faisceaux de parité.
+ Vincent PILAUD Vecteurs dénominateurs et degrés de compatibilité dans les algèbres amassées de type fini 04/03/2013 14:00 001
Dans cet exposé, je présenterai deux descriptions élémentaires des dénominateurs des variables d'amas d'une algèbre amassée de type fini, valables pour un amas initial arbitraire. La première s'exprime en terme des degrés de compatibilité entre les racines presque positives, définis par S. Fomin et A. Zelevinsky. La seconde est basée sur l'interprétation récente des complexes d'amas en termes de complexes de sous-mots, due à C. Ceballos, J.-P. Labbé et C. Stump. Si le temps le permet, je présenterai certains aspects intéressants de cette connexion. Ces descriptions nous fournissent en particulier une preuve simple du fait (connu) que le dénominateur de toute variable d'amas, qui n'est pas dans l'amas initial, a des exposants positifs ou nuls et est différent de 1. Travail en commun avec Cesar Ceballos.
+ Olivier SCHIFFMANN Nombres de points des varietes nilpotentes de Lusztig sur les corps finis 25/02/2013 14:00 001
Nous exprimons le nombre de points sur un corps fini des variétés nilpotentes de Lusztig associées à un carquois, en termes de polynômes de Kac du même carquois. La démonstration se base sur la géométrie des variétés de Nakajima.
+ Louis De THANHOFFER De VÖLCSEY Introduction to Calabi-Yau deformations 18/02/2013 14:00 001
+ Valentin OVSIENKO 1, 2, 4, 8, ?, ??, ... 04/02/2013 14:00 001
La réponse correcte n'est pas ``1, 2, 4, 8, 16, 32, ...'' ! Je parlerai de plusieurs problèmes d'algèbre, combinatoire et géométrie qui ont la solution donnée par la même suite de nombres: la suite de Hurwitz-Radon. Parmi les exemples, le théorème d'Adams sur les champs de vecteurs sur les sphères, les représentations des algèbres de Clifford, les fibrations de Hopf généralisées.
+ Sonia NATALE Exact sequences of tensor categories and applications 28/01/2013 14:00 !201
The talk will be based on joint work with A. Bruguières. We shall discuss the notions of normal tensor functor and exact sequence of tensor categories. Examples of exact sequences of tensor categories arise from (strictly) exact sequences of Hopf algebras, and in particular, from exact sequences of finite groups, and also from equivariantization of a finite tensor category under the action of a finite group. We shall present a classification of exact sequences of tensor categories $C' \to C \to C''$, such that $C'$ is finite, in terms of normal faithful Hopf monads on $C''$. We shall also discuss some applications to classification of fusion categories.
+ Dmitry GOUREVITCH Intertwining operators between line bundles on Grassmanians 14/01/2013 14:00 001
We consider GL(n,R)-equivariant maps between global sections of equivariant line bundles on (possibly) different Grassmanians. We fined when such maps exist and show that they are unique up to a constant. The question and the answer can be formulated in quite elementary terms. Time permitting, I will sketch the proof whose main ingredient is the theory of derivatives that was introduced by Bernstein-Zelevinsky over p-adic fields and recently partially extended to Archimedean fields by us. This is a joint work with Siddhartha Sahi.
+ Masaki KASHIWARA Khovanov-Lauda-Rouquier algebras and R-matrices of quantum affine algebras 17/12/2012 14:00 !005
By using the R-matrices between finite-dimensional modules over a quantum affine algebra, we can construct a functor from the category of finite-dimensional representations of Khovanov-Lauda-Rouquier algebras to the category of finite-dimensional modules over quantum affine algebras. In certain cases, it gives a graded version of the category $C_Q$ of Hernandez-Leclerc. It is a joint work with Seok-Jin Kang and Myugho Kim.
+ Anthony JOSEPH Méandres et Sections de Weierstrass pour les Biparaboliques \ en \ type A 10/12/2012 14:00 001
La forme canonique d'une courbe elliptique admet une présentation comme ``Section de Weierstrass''. Ceci est également le cas pour la description par Kostant des invariants par rapport à l'action co-adjointe d'une algèbre de Lie semi-simple et a été encore généralisé par Popov pour une algèbre de Lie simple agissant sur un module simple dans le cas (plutôt exceptionel) où l'algèbre des invariants est polynomiale. Nous étudions le cas (non-réductif) de l'action co-adjointe d'une sous-algèbre biparabolique de sl(n). Nous avons montré auparavant que l'algèbre des invariants est polynomiale, que la fibre nulle admet un élément régulier et que ceci donne lieu a une Section de Weierstrass. Dans le travail actuel nous montrons que cet élément régulier est l'image d'un élément régulier nilpotent de sl(n). La preuve est purement combinatoire et les méandres ont un rôle prépondérant. Le but est de faire intervenir le groupe de Weyl pour les descriptions des sections de Weierstrass. (Travail avec Florence Millet)
+ Chul-Hee LEE On the boundary of Q-systems : introduction to the KNS conjecture 03/12/2012 14:00 001
The positive solution of the level restricted Q-system plays an important role in dilogarithm identities for conformal field theories. The Kuniba-Nakanishi-Suzuki (KNS) conjecture states that the quantum dimension solution of the Q-system obtained by a certain specialization of classical characters of the Kirillov-Reshetikhin modules gives the positive solution of the level restricted Q-system and has other interesting level truncation properties. In this talk, I will give an introduction to the conjecture and discuss some recent progress.
+ Fernando FANTINO Nichols algebras and pointed Hopf algebras over non-abelian groups 26/11/2012 14:00 001
Nichols algebras play a crucial rôle in the classification of finite-dimensional complex pointed Hopf algebras in the context of Lifting method given by Andruskiewitsch and Schneider. These authors have obtained the classification when the group-likes form an abelian group whose order is relatively prime to 210 ('05). This talk is based on a series of articles concerned with the non-abelian case. I will describe a strategy to approach the classification by means of Nichols algebras coming from a rack and a 2-cocycle. I will show some criteria to decide the dimension of these Nichols algebras and I will presented a list of the results obtained for some families of non-abelian groups. [1] N. Andruskiewitsch, F. Fantino, M. Graña and L. Vendramin, ``Finite-dimensional pointed Hopf algebras with alternating groups are trivial'', Ann. Mat. Pura Appl. (4) 190 2 (2011) 225-245. [2] N. Andruskiewitsch, F. Fantino, M. Graña and L. Vendramin, ``Pointed Hopf algebras over the sporadic simple groups'', J. Algebra 325 1 (2011) 305-320. [3] F. Fantino and G. A. García, ``On pointed Hopf algebras over dihedral groups'', Pacific J. Math., 252 1 (2011), 69-91.
+ Pu ZHANG Homological Identities 19/11/2012 14:00 !201
This talk concerns several homological identities about the Nakayama automorphism of skew Calabi-Yau algebras proved by Brown, Chan, Walton, Rogalski and Meyes during the last few years.
+ Alexis VIRELIZIER Doubles des algèbres de Hopf 12/11/2012 14:00 001
Au début des années 90, Drinfeld a construit le double d'une algèbre de Hopf H, qui est une algèbre quasitriangulaire D(H) telle que sa catégorie des représentations soit équivalente (en tant que catégorie tressée) au centre de la catégorie des représentations de H. Plus généralement, comment construire un tel double lorsque H est une algèbre de Hopf dans une catégorie tressée ? Dans cet exposé je répondrai à cette question. La réponse générale nécessite l'utilisation de la notion de monade de Hopf (qui généralise celle d'algèbre de Hopf).
+ Victoria LEBED Systèmes tressés : généralités et applications à la théorie de Hopf 05/11/2012 14:00 001
Nous présentons la notion de système tressé, qui généralise la notion usuelle de tressage dans une catégorie monoïdale. C'est une famille ordonnée d'objets $V_i$ avec un tressage local, partiel (i.e. défini uniquement sur $V_i \otimes V_j$ avec $i < j$) et non-inversible en général. Nous introduisons et étudions les modules sur les systèmes tressés, ainsi que leurs homologies. Cette théorie abstraite s'applique efficacement à deux problèmes de la théorie de Hopf. 1. La catégorie des bimodules de Hopf sur $H$ est équivalente à celle des modules sur l'algèbre $X$ de C.Cibils et M.Rosso, ou sur les algèbres $Y$ et $Z$ de F.Panaite. Nous incluons ces trois algèbres dans une famille de 24 algèbres mutuellement isomorphes, qui sont en fait des produits tensoriels multi-tressés d'algèbres -- une notion définie pour n'importe quel système tressé d'algèbres. 2. Le complexe bar d'une bigèbre avec des coefficients dans un bimodule de Hopf est un complexe de bimodules de Hopf, avec des structures convenablement définies. Nous montrons que c'est un phénomène général pour l'homologie d'un système tressé à coefficients dans un module sur ce système.
+ Iván ANGIONO About the classification of finite-dimensional pointed Hopf algebras over abelian groups 22/10/2012 14:00 001
The lifting method is a promising program to classify finite-dimensional pointed Hopf algebras. In fact, Andruskiewitsch and Schneider [AS] have used it to obtain the family of all pointed Hopf algebras over the complex numbers, whose coradical is the group algebra of an abelian group of order coprime with 210. It uses the classification of braidings of diagonal type obtained by Heckenberger [H]. In this talk we will present the advances in the general framework, for abelian groups of arbitrary order. It involves the consideration of the Weyl groupoid and a generalized root system for Nichols algebras of diagonal type, coideal subalgebras classified by Heckenberger and Schneider, and convex orders on these roots [A1], in order to have a family of relations between the generators of a PBW basis. A second step involves a minimal presentation by generators and relations needed to prove that any finite dimensional pointed Hopf algebra is generated by group-like elements and skew-primitive elements [A2]. The last step is the computation of all the liftings (that is, all the Hopf algebras associated to a fixed coradically graded Hopf algebras) and uses also this minimal presentation; it is part of a work in progress with N. Andruskiewitsch and A. García Iglesias. [AS] N. Andruskiewitsch and H.-J. Schneider, On the classification of finite-dimensional pointed Hopf algebras, Ann. Math. 171(1) (2010), 375--417. [A1] I. Angiono, A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems, JEMS, to appear. [A2] I. Angiono, On Nichols algebras of diagonal type. J. Reine Angew. Math., to appear. [H] I. Heckenberger, Classification of arithmetic root systems, Adv. Math. 220 (2009), 59--124.
+ Shmuel ZELIKSON Sur les opérateurs cristallins dans les paramétrisations de Lusztig et les inégalités définissant le cone string 15/10/2012 14:00 !005
La base canonique de la partie positive de l'algèbre enveloppante quantifiée $U_q(g)$ admet une action par les opérateurs cristallins de Kashiwara. Cette action permet de munir la base canonique d'une structure combinatoire, le graphe cristallin $B(\infty)$. Si $g$ est de type fini, chaque expression réduite de l'élément le plus long $w_0$ du groupe de Weyl, permet de construire deux paramétrisations de la base canonique : la paramétrisation de Lusztig, utilisant la base PBW associée, et la paramétrisation de Kashiwara, obtenue à partir de la construction élémentaire de $B(\infty)$. Les deux paramétrisations se font par $N$-uplets d'entiers positifs, $N$ étant le nombre de racines positives. Les ensembles paramétrants sont respectivement $N^N$ dans le cas de la paramétrisation de Lusztig, et l'ensemble des points entiers du cone string dans le cas de la paramétrisation de Kashiwara. Les opérateurs cristallins agissent dans la paramétrisation de Lusztig selon un nombre fini de schémas, que l'on peut voir comme des vecteurs de $R^N$. Nous montrons que ces vecteurs induisent un système d'inégalités définissant le cone string, dans le cas g de type $A_n$, et l'expression réduite adaptée à un carquois. Les outils principaux sont les carquois d'Auslander-Reiten et les diagrammes de cordes. Une conséquence directe est que la combinatoire du cone string est décrite directement en termes de la combinatoire des représentations de carquois.
+ Jean-Yves CHARBONNEL Méthode de l'argument translaté et variété commutante 08/10/2012 14:00 001
La méthode de l'argument translaté appliquée au cas des algèbres de Lie réductives permet de construire le module caractéristique pour cette algèbre de Lie. Ce module est libre de rang égal à la dimension des sous-algèbres de Borel. En outre, son orthogonal est également libre. Au moyen du module caractéristique, on construit un complexe d'homologie dont le support de l'homologie est contenu dans la variété commutante. D'un calcul des dimensions projectives des composantes homogènes de ce complexe, on déduit que ce complexe est en fait acyclique. Il en résulte que la variété commutante est normale et Cohen-Macaulay.
+ Fabio GAVARINI Supergroupes algébriques associés aux superalgèbres de Lie de type Cartan 18/06/2012 14:00 001
Pour toute superalgèbre de Lie complexe simple de type Cartan, nous présentons une construction explicite de supergroupes algébriques - donnés par leurs propres foncteurs des points - connexes dont la superalgèbre de Lie tangente est celle de départ. La construction généralise au cas présent la méthode utilisée jadis par Chevalley pour construire des groupes simples connexes associés à toute algèbre de Lie simple de dimension finie. Vice versa, on prouve aussi que tout supergroupe algébrique connexe dont la superalgèbre de Lie tangente soit de type Cartan est isomorphe à l'un des supergroupes donnés par cette construction.
+ Emmanuel LETELLIER Positivité des polynômes de Kac et des invariants DT de carquois 04/06/2012 14:00 001
+ Arturo PIANZOLA Conjugacy theorems in infinite dimensional Lie theory 21/05/2012 14:00 001
We will describe how methods from SGA3 can be used to resolve conjugacy questions regarding Cartan subalgebras of affine and extended affine Kac-Moody Lie algebras.
+ Sophie MORIER-GENOUD Sur un problème de Hurwitz et de communication sans fil 14/05/2012 14:00 001
Adolf Hurwitz aurait-il inventé le wifi ? A la fin du 19ème siècle Hurwitz a formulé un problème connu sous le nom de 'composition de formes quadratiques' ou encore 'identité de sommes de carrés'. Ce problème, encore largement ouvert, s'énonce très simplement en algèbre linéaire et se retrouve lié à de nombreuses questions apparaissant dans des domaines mathématiques variés (topologie, géométrie, théorie des nombres, représentations...). Plus surprenant, les travaux d'Hurwitz sont extremement utilisés en théorie de l'information pour des codages de transmission de données par des réseaux sans fils. Dans cet exposé, nous donnerons un aperçu du problème d'Hurwitz et de diverses applications, en mathématiques et en ingénierie. Nous présenterons une méthode fournissant des solutions basée sur des algèbres non-associatives de type octonions.
+ Olivier SCHIFFMANN L'algèbre de Hall de $\overline{Spec(\mathbb{Z})}$ 07/05/2012 14:00 001
Nous définissons une ``algèbre de Hall'' de faisceaux cohérents sur une compactification de $Spec(\mathbb{Z})$, que nous identifions à une algèbre de battage (de fonctions holomorphes) associé à la fonction zeta de Riemann. C'est un travail en commun avec M. Kapranov et E. Vasserot.
+ Anton ALEKSEEV The Horn problem and planar networks 02/04/2012 14:00 001
+ Matt SZCZESNY Hall algebras and representation theory over the field with one element 26/03/2012 14:00 001
I will describe several examples of non-additive categories where the Hall algebra construction makes sense. These should be viewed as $F_1$ analogues of abelian categories. Examples include categories of Feynman graphs, monoid representations, coherent sheaves on projective monoidal schemes, and quiver representations over $F_1$. The resulting Hall algebras include the Connes-Kreimer Hopf algebra of Feynman graphs and rooted trees and (nilpotent halves of ) enveloping algebras of Kac-Moody and loop algebras.
+ Cédric LECOUVEY Marches aléatoires conditionnées et théorie des représentations 19/03/2012 14:00 001
Le but de l'exposé sera de montrer comment la théorie des représentations des algèbres et super-algèbres de Lie permet de déterminer la loi de marches aléatoires conditionnées à rester dans un cône. Il s'agira aussi d'expliquer comment l'utilisation de résultats probabilistes conduit à déterminer le comportement asymptotique de certaines multiplicités tensorielles liées à la théorie des représentations. Il s'agit d'un travail en collaboration avec E. Lesigne et M. Peigné.
+ Ryosuke KODERA $Ext^1$ for simple modules over $U_q(L\mathfrak{sl}_2)$ 19/03/2012 15:30 001
I talk about a partial result on the calculation of the Ext groups for finite-dimensional simple modules over the quantum loop algerba $U_q(L\mathfrak{sl}_2)$. In particular, the finite-dimensional simple modules that admit nontrivial extensions between the trivial module are determined. I also discuss a refinement of a recent result by Chari-Moura-Young \href{http://arxiv.org/abs/1112.6376}{arXiv:1112.6376}, which establishes a relation between the dimension of the self-extension group and the number of factors in the prime factorization for a simple $U_q(L\mathfrak{sl}_2)$-module.
+ Anthony JOSEPH Les invariants de Zhelobenko et les opérateurs de Bernstein-Gelfand-Gelfand 12/03/2012 14:00 001
+ Grégoire DUPONT Algèbres quasi-amassées de surfaces non-orientables 05/03/2012 14:00 001
A toute surface à bord orientable $S$ munie d'un ensemble fini $M$ de points marqués sur le bord, Fomin, Shapiro et Thurston ont associé une algèbre amassée $A(S,M)$ de sorte que l'ensemble des générateurs naturels de $A(S,M)$ (les variables d'amas) est en bijection avec l'ensemble des arcs dans $(S,M)$. Les relations entre ces générateurs dans $A(S,M)$ correspondent aux relations de longueur entre les arcs correspondants dans $S$. En outre, les variables d'amas sont naturellement regroupés en ensembles de variables compatibles, les amas, correspondant aux triangulations de la surface. Dans le cas où la surface $S$ n'est pas orientable, il n'est pas possible d'utiliser les méthodes de Fomin, Shapiro et Thurston pour construire une algèbre amassée. On peut cependant associer à $(S,M)$ une algèbre ``quasi-amassée'' $A(S,M)$ dont les générateurs correspondent aux ``quasi-arcs'' dans $S$ et se regroupent naturellement en ensembles d'éléments compatibles, les ``quasi-amas'', correspondant aux ``quasi-triangulations'' de $(S,M)$. Les relations entre ces générateurs dans $A(S,M)$ sont données par les relations de longueur entre les quasi-arcs correspondants dans $S$. Lorsque $S$ n'est pas orientable, l'algèbre $A(S,M)$ n'est en général pas amassée. Cependant, nous verrons que les structures quasi-amassées jouissent d'un certain nombre de propriétés analogues à celles des structures amassées. Ceci est un travail conjoint avec Frédéric Palési.
+ Tom BRIDGELAND Stability conditions on $CY_3$ algebras and quadratic differentials 27/02/2012 14:00 001
+ Gleb KOSHEVOY Toric varieties and cluster algebras 20/02/2012 14:00 001
To a framed acyclic quiver, we associate a smooth toric variety. To a cluster algebra of $SL_n/N$, we associate a toric variety (smooth for $n\leq 5$). We will also discuss relations between these two constructions of toric varieties.
+ Pierre BAUMANN Polytopes de Mirković-Vilonen affines (travail en commun avec J. Kamnitzer et P. Tingley) 13/02/2012 14:00 001
+ Fernanda PEREIRA Minimal Affinizations of Quantum Groups 06/02/2012 14:00 001
The concept of minimal affinization, introduced by V. Chari, arose from the impossibility of extending, in general, a representation of the quantum group associated to a simple Lie algebra to the quantum group associated to its loop algebra, which is always possible on the classical context. The classification of the equivalence classes of minimal affinizations is complete when the Lie algebra involved is not of the type D or E, and in type D or E it is done for some cases of highest weight. We present some partial results in the direction of finishing this classification.
+ Tom SUTHERLAND Stability conditions for Painlevé quivers 30/01/2012 14:00 001
To each of the Painlevé equations we associate a quiver drawn on the Riemann sphere by considering trajectories of a one-dimensional family of quadratic differentials with prescribed poles. These quadratic differentials parameterise the base of a Hitchin integrable system whose isomonodromic deformations are described by the solutions of the corresponding Painlevé equation. We will describe a connected component of the space of numerical stability conditions of the Ginzburg algebra of these quivers via the periods of the Seiberg-Witten differential on the spectral elliptic curves.
+ Frédéric CHAPOTON Triangulations de plans projectifs et séries d'algèbres de Lie 23/01/2012 14:00 001
Alors qu'on connait des triangulations minimales des plans projectifs sur $\mathbb{R}$ et sur $\mathbb{C}$, on dispose seulement d'un candidat pour le plan projectif sur les quaternions, et le cas des octonions reste ouvert. Il semble que la théorie des représentations des algèbres de Lie puisse apporter un éclairage nouveau à ce problème.
+ Milen YAKIMOV Multiparameter quantum algebras 09/01/2012 14:00 001
Multiparameter twists of quantum groups and quantum Schubert cell algebras were considered by many authors after the work of Artin, Shelter and Tate. We will prove a conjecture of Brown and Goodearl that the prime ideals of the first class of algebras are completely prime. For the second class of algebras we will prove a conjecture of Goodearl and Lenagan that their H-primes are polynormal, compute the dimensions of the Goodearl-Letzter strata of their spectra, and prove that they are catenary.
+ Giovanni CERULLI Degenerate flag varieties and quiver Grassmannians 12/12/2011 14:30 001
In a recent paper in collaboration with E. Feigin and M. Reineke we investigate the connection beetween flag varieties and their degenerations, with quiver Grassmannians associated with representations of a Dynkin quiver. In previous works, E. Feigin introduced a natural degeneration of (partial) flag varieties. He showed that these varieties are (typically singular) irreducible, normal, local complete intersection which are flat degenerations of the usual flag varieties. Moreover they admit a group action with finitely many orbits and a cellular decomposition. The number of cells equals the (median) Genocchi numbers. In the paper we observed that these varieties are naturally isomorphic to quiver Grassmannians of the form $Gr_{\dim A}(A+A*)$, where $A$ is the path algebra of an equioriented quiver of type A. We hence consider quiver Grassmannians of the form $Gr_{\dim P} (P+I)$, where $P$ and $I$ are respectively a projective and an injective representation of a Dynkin quiver. We find the same properties as for type A. Moreover we compute the Poincaré polynomials of these varieties, finding a natural $q$-version of the median Genocchi numbers.
+ Dragos FRATILA La structure de l'algèbre de Hall d'une courbe elliptique 05/12/2011 14:30 001
+ Ehud MEIR On module categories over graded fusion categories 28/11/2011 14:30 001
Fusion categories arise in several areas of mathematics- such as the representation theory of Hopf algebras and topological quantum field theory. They are tensor categories which satisfy certain rigidity assumptions- they are semisimple, have a finite number of simple objects, and they have duals. A general classification of fusion categories seems to be out of reach at the moment. However, Etingof Nikshych and Ostrik have classified all fusion categories which are extensions of a given fusion category by a given finite group $G$, by cohomological machinery (these are categories which are naturally graded by the group $G$) In this talk I will describe a joint work with Evgeny Musicantov, about the classification of module categories (which, in this setting, are the categorical analogues of modules over a ring) over these fusion categories. I will explain all the fundamental notions, their relevance for the theory of Hopf algebras, and the role that the cohomological machinery plays in the classification.
+ Michael CUNTZ Weyl groupoids and simplicial arrangements 21/11/2011 14:30 001
The Weyl groupoid is a generalization of the Weyl group that appeared in the theory of Nichols algebras. We summarize recent results about these groupoids: the classification of finite Weyl groupoids and the correspondence to certain simplicial arrangements of hyperplanes.
+ Benoit FRESSE Certaines propriétés géométriques des variétés orbitales 14/11/2011 14:30 001
À un élément nilpotent x dans une algèbre de Lie réductive, on peut attacher plusieurs variétés algébriques qui interviennent en théorie des représentations: son orbite nilpotente, l'intersection de cette orbite nilpotente avec une sous-algèbre de Borel (les composantes irréductibles de cette intersection sont appelées variétés orbitales), ou la fibre au dessus de x de la résolution de Springer. Il y a un lien étroit entre la fibre de Springer de x et les variétés orbitales associées à x. Dans cet exposé, on s'appuie sur ce lien pour étudier deux propriétés des variétés orbitales: la propriété d'être lisse, et la propriété de contenir une B-orbite dense. Pour le type A, on donne plusieurs critères qui suggèrent une relation entre ces deux propriétés.
+ Damien CALAQUE Théorèmes de PBW et auto-intersections dérivées 07/11/2011 14:30 001
J'expliquerai comment décrire explicitement l'algèbre des fonctions de l'auto-intersection dérivée d'une sous-variété algébrique $X\subset Y$ comme le dual de l'algèbre enveloppant d'un algébroïde de Lie approprié. Si le temps le permet je présenterai quelques applications. Il s'agit d'un travail en cours avec Andrei Caldararu et Junwu Tu.
+ Jérémy BLANC Sur le groupe des transformations symplectiques du plan complexe 31/10/2011 14:30 001
Une transformation symplectique du plan complexe $C^2$ est une transformation birationnelle qui préserve la forme différentielle canonique $dx/x \wedge dy/y$. Je tâcherai d'expliquer pourquoi ce groupe est engendré par les applications monomiales et par une application spéciale d'ordre 5 $(x,y) \mapsto (y,(y+1)/x)$, résultat conjecturé par A. Usnich.
+ Amnon YEKUTIELI Cohomologically complete complexes 24/10/2011 14:30 001
Let $A$ be a noetherian commutative ring, and $\mathfrak{a}$ an ideal in it. In this lecture I will talk about several properties of the derived $\mathfrak{a}$-adic completion functor and the derived $\mathfrak{a}$-torsion functor. In the first half of the talk I will discuss $\mathfrak{a}$-adically projective modules, GM Duality (first proved by Alonso, Jeremias and Lipman), and the closely related MGM Equivalence. The latter is an equivalence between the category of cohomologically $\mathfrak{a}$-adically complete complexes and the category of cohomologically $\mathfrak{a}$-torsion complexes. These are triangulated subcategories of the derived category D(Mod $A$). In the second half of the talk I will discuss new results: (1) A characterization of the category of cohomologically $\mathfrak{a}$-adically complete complexes as the right perpendicular to the derived localization of $A$ at $\mathfrak{a}$. This shows that our definition of cohomologically $\mathfrak{a}$-adically complete complexes coincides with the original definition of Kashiwara and Schapira. (2) The Cohomologically Complete Nakayama Theorem. (3) A characterization of cohomologically cofinite complexes. (4) A theorem on completion by derived double centralizer. This is joint work with Marco Porta and Liran Shaul.
+ Philip BOALCH Irregular connections, Dynkin diagrams and fission 17/10/2011 14:30 001
+ David HERNANDEZ Catégorification de $\mathbb{C}[N]$ par des représentations de $U_q(L\mathfrak{g})$ 10/10/2011 14:30 001
+ Maxim KONTSEVICH Sur la symétrie miroir pour les systèmes intégrables complexes 06/06/2011 14:30 001
séance commune avec la journée ``quant X - Paris 7''
+ Raf BOCKLANDT Generating toric noncommuative crepant resolutions 30/05/2011 14:30 001
We introduce an algorithm that can generate all toric noncommutative crepant resolutions of a 3-dimensional toric Gorenstein variety and represent them as dimer models. We discuss how the algorithm can be generalized to the non-gorenstein and higher dimensional cases and if timing allows it, we explore its connection with mirror symmetry.
+ Michel DUBOIS-VIOLETTE Préalgèbres et préalgèbres de Lie 23/05/2011 14:30 001
On définit une notion générale de préalgèbre, puis plus spécifiquement une notion de préalgèbre de Lie qui capture en particulier les diverses généralisations des algèbres de Lie liées aux groupes quantiques. La dualité de Koszul due à Positselski pour les algèbres quadratiques non homogènes permet de faire le lien avec le calcul différentiel sur les groupes quantiques
+ Fabio GAVARINI Quantification d'espaces projectifs homogènes et applications 16/05/2011 14:30 001
Soient $G$ un groupe de Poisson et $M$ un $G$-espace homogène projectif muni d'une structure de Poisson quotient de celle de $G$ (ce qui revient à dire que $M = G/K$ où $K$ est un sous-groupe coïsotrope de $G$). Je présenterai une recette générale pour construire -- à partir d'un minimum de données -- une quantification de $M$ en tant qu'espace homogène, donc à la fois de $M$ (en tant qu'espace projectif) et de l'action de $G$ sur $M$. Ensuite, je montrerai comment on peut formuler (et prouver) un ``principe de dualité quantique'' convenable lequel, à partir d'une quantification de $M = G/K$ au sens qu'on vient de décrire, nous donne une quantification de l'espace homogene ``dual'' pour un groupe de Poisson dual de $G$ (par rapport à la dualité de Poisson). Enfin, je montrerai comment l'exemple des grassmanniennes quantiques et l'exemple des variétés de drapeaux (généralisés) quantiques peuvent être retrouvés comme cas particuliers de cette construction générale.
+ Frédéric CHAPOTON Sur une opérade ternaire liée aux treillis de Tamari 02/05/2011 14:30 001
+ Antonin GUILLOUX Tétraèdres de drapeaux et représentations de variétés de dimension 3 04/04/2011 14:30 001
On définira des coordonnées inspirées des travaux de Fock et Goncharov pour un tétraèdre de drapeaux. Cela permet de munir l'espace des représentations d'une variété de dimension 3 dans $SL(3,\mathbb{C})$ d'une notion de volume et d'une structure symplectique. On s'inspire des travaux de Neumann et Zagier pour montrer que cette structure est isomorphe à une structure naturelle sur les représentations du bord de la variété.
+ Sergey MOZGOVOY On Donaldson-Thomas invariants for quivers with potentials 21/03/2011 14:30 001
+ Loïc FOISSY Algèbres de Hopf libres et colibres 14/03/2011 14:30 001
La théorie des algèbres de Hopf combinatoires a fait apparaître un certain nombre d'algèbres de Hopf libres et colibres, provenant de différents domaines : physique mathématiques (algèbres non commutatives d'arbres de Connes-Kreimer), combinatoires ou fonctions symétriques (algèbres des permutations FQSYm, algèbres de composition...), opérades (algèbres dendriformes, algèbres 2-As...). Tous ces objets sont gradués, connexes, et il a été démontré par différents moyens que deux des objets précédemment cités ayant la même série formelle sont isomorphes. Les preuves utilisent, soit des isomorphismes explicites, soit des méthodes de scindement d'associativité. Nous donnons une preuve plus générale de ce résultat et montrons que deux algèbres de Hopf libres et colibres sont isomorphes (en tant qu'algèbres de Hopf graduées) si, et seulement si, elles ont la même série formelle. D'autre part, nous montrons que l'algèbre de Lie des éléments primitifs d'une algèbre de Hopf libre et colibre est libre et nous en déduisons une caractérisation des séries formelles d'algèbres de Hopf libres et colibres. Enfin, nous montrons que deux telles algèbres de Hopf sont isomorphes (de façon non graduée), si, et seulement si, leurs algèbres de Lie ont le même nombre de générateurs.
+ Guillaume POUCHIN Fibrés de Higgs et algèbres de Lie affines 07/03/2011 14:30 001
+ Daniel LABARDINI-FRAGOSO Quivers with potentials from triangulated surfaces 28/02/2011 14:30 001
We give an elementary construction of quivers with potentials for (ideal) triangulations of surfaces with marked points, in such a way that triangulations related by a flip give rise to QPs related by Derksen-Weyman-Zelevinsky mutation. These QPs are non-degenerate provided the surface has non-emtpy boundary. We also give an elementary construction of representations of these QPs that correspond to cluster variables of the cluster algebra associated to the surface by Fomin-Shapiro-Thurston.
+ Hideto ASASHIBA Derived equivalences and Grothendieck constructions of lax functors 14/02/2011 14:30 001
+ Peng SHAN Algèbres de Heisenberg et algèbres de Cherednik rationnelles 07/02/2011 14:30 001
+ Travis SCHEDLER Computational approaches to Poisson traces on quotient singularities 31/01/2011 14:30 001
Poisson traces are linear functionals on a Poisson algebra which annihilate Poisson brackets. They are dual to the zeroth Poisson (or Lie) homology, and the dimension of this space bounds the number of irreducible finite-dimensional representations of any quantization. I will consider the case where the Poisson algebra is the algebra of $G$-invariant polynomials in $2n$ variables with complex coefficients, where $G$ is a finite subgroup of $Sp(2n,C)$. I will prove some results which reduce the computation of Poisson traces, for fixed $n$ and $G$, to a finite one that can be done by computer, and will describe several results of this computation. I will also classify the complex reflection groups $G$ for $n = 2$ for which the dimension of the Poisson traces coincides with the (well-known) dimension of the zeroth Hochschild homology of the algebra of $G$-invariant differential operators in n variables, which a priori is only a lower bound. The results also imply this equality for Coxeter groups of rank $\leq 3$ and the Weyl groups $B_4$ and $D_4$. These results also give the Hilbert series of the space of Poisson traces, in terms of the polynomial degree (and when the aforementioned equality holds, also this series for the zeroth Hochschild homology). This is joint work with Etingof, Gong, Pacchiano, and Ren, part of which took place in the context of undergraduate research at MIT.
+ Earl TAFT Quelques suites polynomialement récurrentes et identités combinatoires 24/01/2011 14:30 001
+ Xin FANG Les algèbres $q$-bosons 17/01/2011 14:30 001
+ relâche en raison de l'exposé de H. Nakajima à l'IHP 10/01/2011 14:30 001
+ Thilo GRUNWALD-HENRICH Vector bundles on genus one curves and Yang-Baxter equations 03/01/2011 14:30 001
+ Anthony JOSEPH Paires adaptées et éléments principaux nilpotents 06/12/2010 14:30 001
+ Christof GEISS Tubular cluster algebras 29/11/2010 14:30 001
+ Claire AMIOT Equivalence dérivée et mutation graduée 22/11/2010 14:30 001
+ Michel van den Bergh Calabi-Yau algebras and superpotentials 15/11/2010 14:30 001
+ Ben DAVISON Superpotential algebras and manifolds 08/11/2010 14:30 001
+ Stéphane LAUNOIS Matrices quantiques et positivité totale 25/10/2010 14:30 001
+ Sophie MORIER-GENOUD Espaces de polygones dans le plan projectif, de frises algébriques, et leur structure de variétés amassées 11/10/2010 14:30 001
+ Alek VAINSHTEIN Cluster algebras and Poisson geometry 04/10/2010 14:30 001
+ Pavel ETINGOF $D$-modules on Poisson varieties and Poisson traces 28/06/2010 14:00 !0D1 à Chevaleret
+ Anthony JOSEPH Les règles de somme pour les invariants générateurs 28/06/2010 17:30 !0C2 à Chevaleret
+ Ivan LOSEV Completions of symplectic reflection algebras 28/06/2010 15:30 !0D1 à Chevaleret
+ Frédéric CHAPOTON Sur le spectre des algèbres amassées 21/06/2010 14:30 001
Où il sera question de morphismes vers un espace affine, de points sur les corps finis et de cohomologie à support compact.
+ Philipp LAMPE A quantum cluster algebra of Kronecker type and the dual canonical basis 14/06/2010 14:30 001
+ Jan SCHRÖER Generic bases for cluster algebras and the Chamber Ansatz 31/05/2010 14:30 001
+ Damien CALAQUE Dualité de Koszul et quantification par déformation 17/05/2010 14:30 001
+ Michel van den Bergh Representation theory of noncommutative quantum groups 22/03/2010 14:30 001
+ Daisuke YAMAKAWA Quiver varieties with multiplicities and Weyl groups of non-symmetric Kac-Moody algebras 15/03/2010 14:30 001
+ Simon RICHE Variété de Steinberg, algèbres de Hecke et algèbres de Lie semi-simples en caractéristique positive 08/03/2010 14:30 001
Il est bien connu (et dû à Kazhdan-Lusztig et Ginzburg) que la géométrie de la variété de Steinberg associée à un groupe algébrique semi-simple ``gouverne'' la théorie des représentations de l'algèbre de Hecke affine associée. Plus récemment, des travaux de Bezrukavnikov-Mirkovic-Rumynin ont montré que cette géométrie joue également un rôle essentiel dans la théorie des représentations de l'algèbre de Lie du groupe en caractéristique positive. Dans cet exposé je présenterai des travaux en collaboration avec Bezrukavnikov qui permettent d'expliciter les liens entre ces 2 théories, à travers une action du groupe de tresses affine sur certaines catégories de faisceaux cohérents.
+ Pedro NICOLÁS $t$-structures et objets simplistes pour les algèbres différentielles graduées 01/03/2010 14:30 001
+ Olivier SCHIFFMANN Algèbres de Hall des courbes et dualité de Langlands géométrique 22/02/2010 14:30 001
Nous considérons une algèbre de convolution dans l'espace des fonctions sur les champs de modules $Bun_{GL_r}X$ de fibrés sur une courbe projective lisse $X$, et nous en donnons une réalisation algébrique en termes d'algèbre de battage (similaire a certaines algèbres introduites par Feigin et Odesskii). D'un autre coté, nous construisons une algèbre de convolution dans la $K$-theorie équivariante des variétés de représentations (infinitésimales) du groupe fondamental de $X$ dans les groupes $GL_r$, dont nous donnons aussi une présentation à l'aide d'algèbres de battage. L'isomorphisme entre ces deux types d'algèbres s'interprète comme une dualité de Langlands géométrique. Il s'agit d'un travail en collaboration avec É. Vasserot.
+ Thomas BRÜSTLE From Christoffel words to Markoff numbers 15/02/2010 14:30 001
+ David HERNANDEZ Dualité de Langlands et algèbres affines quantiques 08/02/2010 14:30 001
+ Alexander ZIMMERMANN Conjecture d'Auslander-Reiten et homologie de Hochschild stable 18/01/2010 14:30 001
+ Slava FUTORNY Gelfand-Tsetlin modules over Galois algebras 11/01/2010 14:30 001
The talk is based on joint results with S. Ovsienko. We will discuss Gelfand-Tsetlin modules for a class of Galois algebras which are certain invariant subalgebras in skew group rings. In particular, examples of the universal enveloping algebra of $\mathfrak{gl}(n)$ and finite $W$-algebras of type $A$ will be considered. As an application, we obtain an analog of the Gelfand-Kirillov conjecture for above mentioned algebras.
+ Sarah SCHEROTZKE Sur les carquois d'Auslander-Reiten des catégories dérivées 04/01/2010 14:30 001
+ Wolfgang BERTRAM Géométries associatives 14/12/2009 14:30 001
+ Shreeram S. ABHYANKAR Dictritical divisors and Jacobian problem 07/12/2009 14:30 001
+ Thomas WILLWACHER A Drinfeld associator and formality of the little disks operad 30/11/2009 14:30 001
+ Kentaro NAGAO Caldero-Chapoton formula via Donaldson-Thomas theory 23/11/2009 14:30 001
Kontsevich and Soibelman observed that the cluster transformation appears in the transformation formula of noncommutative Donaldson-Thomas invariants under a mutation. Generalizing this observation I provide a transformation formula of noncommutative Donaldson-Thomas invariants under tilting, which implies a Caldero-Chapoton-type formula for compositions of cluster transformations.
+ Philippe DI FRANCESCO Towards non-commutative cluster algebras 16/11/2009 14:30 001
+ Alexander PREMET On the Gelfand-Kirillov conjecture for simple Lie algebras 09/11/2009 14:30 001
+ Ken BROWN On the ubiquity of (Auslander) Gorenstein rings 02/11/2009 14:30 001
+ Lesya BODNARCHUK Representations of boxes and brick-tame categories 26/10/2009 14:30 001
+ Anton KHOROSHKIN Grobner bases and monomial resolutions for (di)-operads 19/10/2009 14:30 001
+ Claire LEVAILLANT Réductibilité de la représentation de Lawrence-Krammer 12/10/2009 14:30 001
+ Manolo SAORÍN Small object argument, cotorsion pairs and adjoints in homotopy categories 05/10/2009 14:30 001
+ Markus REINEKE Quivers and Donaldson-Thomas type invariants 08/06/2009 14:30 001
+ Earl TAFT La correspondance boson-fermion et les groupes quantiques unilatères 25/05/2009 14:30 001
+ Michela VARAGNOLO Algèbres KLR et bases canoniques 04/05/2009 14:30 001
+ Leonid POSITSELSKI Koszul Triality 06/04/2009 14:30 001
+ Patrick LE MEUR Degré des morphismes irréductibles et type de représentation 30/03/2009 14:30 001
+ István HECKENBERGER Weyl groupoids 23/03/2009 14:30 001
+ Nicolas RESSAYRE GIT-cones et applications 16/03/2009 14:30 001
Résumé : Soit $G$ un groupe complexe réductif agissant sur une variété projective. On s'interesse au cône convexe engendré par les fibrés en droites (amples) $G$-linéarisés qui admettent des sections $G$-invariantes non nulles. Nous verrons des applications au problème de Horn généralisé (à d'autres groupes que $U_n$ ainsi que dans le langage des carquois). Si le temps le permet nous présenterons aussi quelques conséquences sur les coefficients de structure de certaines grassmanniennes.
+ relâche 09/03/2009 14:30 001
+ relâche 02/03/2009 14:30 001
+ Alessandro RUZZI Variétés symétriques lisses compactes avec nombre de Picard un 23/02/2009 14:30 001
+ Serge PELAP Les propriétés homologiques des algèbres elliptiques de petite dimension 16/02/2009 14:30 001
L'auteur calcule l'homologie et la cohomologie de Poisson d'une structure Jacobienne de Poisson en dimension quatre, donnée par deux Casimirs quasi-homogènes formant une intersection complète à singularité isolée. Les cas de Sklyanin en est un cas particulier. Grâce à la dégénèrescence de la suite spectrale de Brylinski, il obtient l'homologie de Hochschild de la ``vraie'' algèbre de Sklyanin à quatre générateurs ``quantiques''. L'auteur parlera également des résultats sur la classification des structures de Poisson quadratiques invariant par rapport à l'action naturelle du groupe d'Heisenberg sur l'algèbre des polynômes et il est aussi établi que ces structures sont unimodulaires et une certaine relation de Cremona en dimension cinq entre les algèbres de Poisson, définies par Odesskii et Feigin.
+ Nicolás ANDRUSKIEWITSCH Algèbres de Hopf pointées de groupes non abéliens 09/02/2009 14:30 001
+ Laurent DEMONET Catégorification d'algèbres amassées antisymétrisables et application aux sous-groupes unipotents des groupes de Lie semi-simples 02/02/2009 14:30 001
+ Bernard LECLERC Cellules unipotentes et algèbres amassées 26/01/2009 14:30 001
+ Dieter VOSSIECK Rigid homomorphisms between finite abelian $p$-groups 19/01/2009 14:30 001
+ Charles TOROSSIAN Formule explicite pour le problème de Kashiwara-Vergne 12/01/2009 14:30 001
+ Jacob GREENSTEIN Les carquois associés avec certaines algèbres de $\mathfrak{g}$-invariants 05/01/2009 14:30 001
+ Sophie MORIER-GENOUD Relèvement géométrique de la base canonique 08/12/2008 14:30 001
+ Anthony JOSEPH La formule de Weyl-Kac-Borcherds dans le cadre des chemins de Littelmann 01/12/2008 14:30 001
+ Steffen KÖNIG Cellular structures and affine Hecke algebras 24/11/2008 14:30 001
+ Edward FRENKEL Opers with irregular singularity and shift of argument subalgebra 17/11/2008 14:30 001
The universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras. Recently B. Feigin, L. Rybnikov and myself have proved that generically their action on finite-dimensional modules is diagonalizable and their joint spectra are in bijection with differential geometric objects on the projective line called ``opers''. They have regular singularity at one point, irregular singularity at another point and are monodromy free. Interestingly, they are associated not to G, but to the Langlands dual group of G. In addition, we have shown that the quantum shift of argument subalgebra corresponding to a regular nilpotent element of g has a cyclic vector in any irreducible finite-dimensional g-module. As a byproduct, we obtain the structure of a Gorenstein ring on any such module. I will talk about these results and explain their connection to the geometric Langlands correspondence.
+ Damien CALAQUE L'isomorphisme de Duflo, la classe d'Atiyah, et la conjecture de Caldararu 10/11/2008 14:30 001
+ Sergey MOZGOVOY DT invariants and $3$-Calabi-Yau algebras 27/10/2008 14:30 001
+ Ivan MARIN Algèbres de Hecke infinitésimales 20/10/2008 14:30 001
+ Benjamin WILSON A character formula for Chari's category $\widetilde{\mathcal{O}}$ 13/10/2008 14:30 001
One may construct, for any function on the integers, an irreducible module of level zero for affine $sl(2)$ using the values of the function as structure constants. The modules constructed using exponential polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category $\tilde{O}$ of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.
+ Hugh THOMAS ``Dual'' Garside structures for finite-type Artin groups via quiver representations 06/10/2008 14:30 001
The Artin groups of type A are the braid groups; for any Coxeter group, there is an associated Artin group, which is called finite type if the Coxeter group is finite.There is a standard presentation for Artin group analogous to the standard presentation for Coxeter groups. A useful property of the standard presentation for Artin groups of finite type is that there is an associated Garside structure. This gives, for example, an algorithm for computing a normal form for elements of the Artin group. \par Bessis introduced a ``dual'' presentation for finite type Artin groups (extending work of Birman-Ko-Lee in type A) which also has this Garside property, and which is, in some respects, computationally preferable. The proofs of Bessis's results make use of type-by-type arguments and computer checks for the exceptional types. I will explain an alternative approach to this Garside structure (in crystallographic cases only) using the representation theory of Dynkin quivers in which the proofs are carried out in a uniform way. Time permitting, I will also discuss conjectural applications to non-finite-type Artin groups.
+ Julien BICHON Groupes quantiques opérant sur 4 points 16/06/2008 14:30 001
+ Karin BAUR Adjoint $P$-orbits for orthogonal groups 09/06/2008 14:30 001
+ Charles TOROSSIAN L'équation pentagonale dans $sder_3$ et $kv_3$ et ses conséquences 02/06/2008 14:30 001
+ Micha PEVZNER Crochets de Rankin-Cohen et quantification des espaces symétriques. 26/05/2008 14:30 001
+ Stefan MAUBACH The polynomial automorphism group : polynomial automorphisms over finite fields and locally finite polynomial maps. 19/05/2008 14:30 001
+ Olivier SCHIFFMANN Séries d'Eisenstein géométriques et polynômes de Macdonald. 05/05/2008 14:30 001
+ Markus REINEKE Poisson automorphisms and quiver moduli 21/04/2008 14:30 001
+ Michel DUBOIS-VIOLETTE Potentiels généralisés et algèbres graduées de Koszul-Gorenstein. 31/03/2008 14:30 001
+ Stéphane LAMY Automorphismes de surfaces non compactes et théorie de Mori. 17/03/2008 14:30 001
+ Roland BERGER Un théorème de Gerasimov appliquée aux algèbres N- Koszul. 10/03/2008 14:30 001
+ Gérard CAUCHON Diagrammes admissibles dans les déformations quantiques d'algèbres de Lie nilpotentes. 03/03/2008 14:30 001
+ I. GORDON The Gelfand-Kirillov conjecture for symplectic reflection algebras 25/02/2008 14:30 001
+ Nikita MARKARIAN On a (super)geometric fact that follows the Duflo formula and others 11/02/2008 14:30 001
+ Atsushi TAKAHASHI Finite dimensional algebras associated to hypersurface singularities 04/02/2008 14:30 001
+ Caroline GRUSON Formule des caractères pour les superalgèbres de Lie basiques classiques 28/01/2008 14:30 001
+ Steffen SAGAVE DG algebras and derived $A_\infty$-algebras 21/01/2008 14:30 001
+ Bernard LECLERC Algèbres amassées et algèbres quantiques affines 14/01/2008 14:30 001
Des notes sont disponibles ici : \href{http://www.imj-prg.fr/gr/PHP/notes/2007-2008/LeclercExpoIHP08.pdf}{http://www.imj-prg.fr/gr/PHP/notes/2007-2008/LeclercExpoIHP08.pdf}
+ Geert van De WEYER Double Poisson Cohomology 17/12/2007 14:30 001
+ Bruno VALLETTE Théorie de déformation des morphismes de props 10/12/2007 14:30 001
Pour tout morphisme de props, nous définirons, à la Quillen, un complexe de chaines qui mesure les déformations de ce morphisme. Lorsque le prop but est le prop des endomorphismes d'un module A, ceci définit la théorie homologique des déformations de A comme (bi)gèbre sur le prop source. Nous retrouvons de cette manière les différents complexes de chaines de la littérature : (co)homologie de Hochschild des algèbres associatives, de Chevalley-Eilenberg des algèbres de Lie, de Harrison des algèbres commutatives, de Lecomte-Roger des bigèbres de Lie, de Gerstenhaber-Schack des bigèbres associatives. Grâce à ce point de vue, nous monterons que ce complexe de chaines est toujours une algèbre de Lie à homotopie près (stricte lorsque le prop est de Koszul). Les solutions de Maurer-Cartan généralisées correspondent alors aux structures déformées de (bi)gèbre sur A. De plus, nous construirons des opérations supérieures (non binaires) agissant sur ce complexe qui généralisent les opérations braces du complexe de Hochschild. Ceci nous permettra de montrer une version généralisée de la conjecture de Deligne.
+ Charles TOROSSIAN Des équations de Kashiwara-Vergne aux associateurs géométriques 19/11/2007 14:30 001
+ Vladimir BAVULA The Jacobian Algebras 12/11/2007 14:30 001
+ Vladimir HINICH Drinfeld double of an orbifold 05/11/2007 14:30 001
+ Lutz HILLE Group actions with a dense orbit and the volume of a tilting module 29/10/2007 14:30 001
+ Bernt Tore JENSEN Exceptional representations for a double of quiver of type $A$ and Richardson elements in seaweed Lie algebras 15/10/2007 14:30 001
+ Claude CIBILS Le groupe fondamental intrinsèque d'une catégorie linéaire 08/10/2007 14:30 001
+ Maxim KONTSEVICH Stability conditions, Donaldson-Thomas invariants and cluster transformations 04/06/2007 14:30 !amphi Hermite
Exceptionnellement en amphi Hermite, de 14h30 à 16h
+ Philippe BONNET Sur les automorphismes algébriques et leurs invariants rationnels 21/05/2007 14:30 001
Le but de cet exposé est d'étudier les automorphismes de variétés algébriques qui ont en un sens ``beaucoup d'invariants'', et de montrer que ces derniers proviennent d'actions algébriques de groupes algébriques. On se donne une variété affine irréductible $X$ sur un corps $k$ algébriquement clos de caractéristique nulle. Si $\Phi$ est un automorphisme de $X$, on désigne par $k(X)^{\Phi}$ son corps des invariants, c'est-à-dire l'ensemble des fonctions rationnelles $f$ sur $X$ pour lesquelles $f\circ \Phi=f$, et par $n(\Phi)$ le degré de transcendance de $k(X)^{\Phi}$ sur $k$. Nous allons décrire la classe des automorphismes $\Phi$ pour lesquels $n(\Phi)=\dim X -1$. Plus précisément, nous allons montrer que, sous certaines conditions sur $X$, tout automorphisme de ce type est de la forme $\Phi=\varphi_g$, où $\varphi$ est une action algébrique sur $X$ d'un groupe linéaire de dimension 1, et où $g$ est un élément de $G$. Ensuite, nous verrons des applications de ce résultat à certains automorphismes de $k^2$ et de $k^3$, et nous examinerons le cas où $k$ n'est plus algébriquement clos de caractéristique nulle.
+ Georges PINCZON Deux applications du produit de Moyal 07/05/2007 14:30 001
+ Jan SCHRÖER Tilting theory and cluster algebras 30/04/2007 14:30 001
+ Alexander ROSENBERG Noncommutative algebraic geometry and construction of representations 02/04/2007 14:30 001
+ Markus REINEKE Smooth models of quiver moduli 26/03/2007 14:30 001
+ Nicolas GUAY Carquois et algèbres doublement affines 19/03/2007 14:30 001
+ Wendy LOWEN On deformations of derived categories 12/03/2007 14:30 001
+ Patrick LE MEUR Du revêtement universel à la simple connexité des algèbres héréditaires par morceaux 05/03/2007 14:30 001
+ Idun REITEN Preprojective algebras and Calabi-Yau categories 26/02/2007 14:30 001
+ R. FARNSTEINER Recent developments in support spaces and representation theory 19/02/2007 14:30 001
+ Yuri BEREST Ideals of rings of differential operators on smooth curves 12/02/2007 14:30 001
There is a simple geometric classification of ideals of the 1st complex Weyl algebra, called the Calogero-Moser Correspondence. In this talk I will explain a global version of this construction, replacing the Weyl algebra by the ring of global differential operators on a smooth affine curve. This is joint work with George Wilson (Oxford).
+ Andrey LAZAREV Characteristic classes of $A_\infty$-algebras 05/02/2007 14:30 001
+ Aurélien DJAMENT Représentations des groupes linéaires, foncteurs en grassmanniennes et filtration de Krull 29/01/2007 14:30 001
Nous rappellerons le rôle joué par la catégorie $F$ des foncteurs entre espaces vectoriels sur un corps fini $k$, dite des représentations génériques des groupes linéaires sur $k$, dans l'étude cohomologique de ces groupes linéaires (avec les travaux de Betley-Suslin, notamment). Les objets de longueur finie de la catégorie $F$ sont assez bien connus, mais sa structure globale reste très mystérieuse. Nous présenterons une description conjecturale de la filtration de Krull de $F$, à l'aide de nouvelles catégories, dites catégories de foncteurs en grassmanniennes. Celles-ci nous permettront également de donner une propriété nouvelle en cohomologie fonctorielle.
+ André HENRIQUES La périodicité de la récurrence de l'octaèdre 22/01/2007 14:30 001
La récurrence de l'octaèdre vit sur un réseau à 3 dimensions et s'écrit $f(x,y,t+1):=(f(x+1,y,t)f(x-1,y,t)+f(x,y+1,t)f(x,y-1,t))/f(x,y,t-1)$. Nous étudions une variante qui vit dans le domaine $[0,n] \times [0,m] \times \mathbb{R}$ et prouvons qu'elle est périodique de période $n+m$.
+ Frédéric CHAPOTON Opérade des modules et modules basculants 08/01/2007 14:30 001
+ David HERNANDEZ Théorème d'élimination - applications au problème géométrique de petitesse et aux affinisations minimales de représentations 18/12/2006 14:30 001
+ Philippe CALDERO Grassmanniennes de sous-modules et applications 11/12/2006 14:30 001
+ Yuly BILLIG Solving non-commutative differential equations in vertex algebras 04/12/2006 14:30 001
+ Stéphane LAUNOIS Homologie et cohomologie de Poisson : une dualité tordue 27/11/2006 14:30 001
+ Toby STAFFORD Noncommutative Projective Surfaces 13/11/2006 14:30 001
+ Christof GEISS From preprojective to quasi-hereditary algebras 30/10/2006 14:30 001
+ Pu ZHANG Serre duality and Calabi-Yau categories 23/10/2006 14:30 001
+ Loïc FOISSY Bigèbres bidendriformes, fonctions quasi-symétriques libres et arbres enracinés plans 16/10/2006 14:30 001
+ Amnon YEKUTIELI Weak Deformations of Algebraic Varieties 09/10/2006 14:30 001
+ Michel van den Bergh The singularities of the center of an order of finite global dimension 19/06/2006 14:30 001
+ Robert WISBAUER Corings and Galois comodules 12/06/2006 14:30 001
+ Osamu IYAMA Mutation and tilting modules over Calabi-Yau algebras 29/05/2006 14:30 001
+ Alexander SAMOKHIN Fibrés basculants sur les variétés de Fano via le morphisme de Frobenius 22/05/2006 14:30 001
+ Ken GOODEARL Symplectic leaves, torus orbits, and Bruhat cells in matrix varieties 15/05/2006 14:30 001
+ Guido PEZZINI Sur les classifications des variétés sphériques et magnifiques 15/05/2006 16:00 001
+ Gilles HALBOUT Quantification des twists et des bigèbres de Lie cobord 24/04/2006 14:30 001
+ Sébastien FOULLE Application des paires duales de groupes algébriques au calcul des caractères en caractéristique naturelle 03/04/2006 14:30 001
+ Xavier YVONNE Bases canoniques d'espaces de Fock de niveau supérieur et $v$-algèbres de Schur cyclotomiques 27/03/2006 14:30 001
+ Arzu BOYSAL Picard group of Moduli spaces of semistable $G$-bundles on curves 20/03/2006 14:30 001
+ Charles TOROSSIAN Quantification de Cattaneo-Felder : application à la construction de caractères 13/03/2006 14:30 001
+ Raf BOCKLANDT Graded Calabi-Yau algebras of dimension 3 06/03/2006 14:30 001
+ Emanuela PETRACCI Sur la conjecture de Kashiwara-Vergne 27/02/2006 14:30 001
+ Nicolás ANDRUSKIEWITSCH Catégories tensorielles attachées aux groupoïdes doubles 13/02/2006 14:30 001
+ Bernhard KELLER Algèbres amassées et catégories triangulées 30/01/2006 14:30 001
+ Charlotte DEZÉLÉE Dualité de Schur-Weyl et algèbres de Cherednik 23/01/2006 14:30 001
+ Christian KASSEL Extensions galoisiennes de Hopf et identités polynomiales 16/01/2006 14:30 001
+ Boris FEIGIN Derived functor of a factor-algebra over 2nd commutant 09/01/2006 14:30 001
+ Frédéric CHAPOTON Opérades cycliques et translation d'Auslander-Reiten 12/12/2005 14:30 001
+ Anne PICHEREAU Cohomologie de Poisson en petites dimensions 05/12/2005 14:30 001
+ Philippe CALDERO Algèbre de Hall de certaines catégories de Calabi-Yau 28/11/2005 14:30 001
+ Michael BAROT On the Grothendieck group of a cluster category of a canonical algebra 21/11/2005 14:30 001
+ Pierre-Marie POLONI Plongements des hypersurfaces de Danielewski et leurs conséquences 14/11/2005 14:30 001
+ Wendy LOWEN Deformations of ringed spaces 07/11/2005 14:30 001
+ Damien CALAQUE Quantification des $r$-matrices dynamiques via la formalité 31/10/2005 14:30 001
+ Roland BERGER Algèbres de réflexion symplectiques supérieures et théorème PBW 24/10/2005 14:30 001
+ Oleksandr KHOMENKO Projective functors and characters of tilting modules 10/10/2005 14:30 001
+ Michel DUFLO Variétés associées pour les superalgèbres de Lie 03/10/2005 14:30 001
+ Valerio TOLEDANO LAREDO Algèbres de quasi-Coxeter, cohomologie de Dynkin et groupes de Weyl quantiques 06/06/2005 14:30 001
+ Uri ONN Some remarks on the representation theory of $GL(n,\mathcal{O})$ 30/05/2005 14:30 001
+ Koen De NAEGHEL On the Hilbert scheme of points on quantum projective planes 23/05/2005 14:30 001
+ Relâche 16/05/2005 14:30 001
+ Vasiliy DOLGUSHEV Hochschild cohomology versus orbifold cohomology 09/05/2005 14:30 001
+ Alberto CATTANEO Superformality and Quantization 04/04/2005 14:30 001
+ Rudolf RENTSCHLER Une réponse négative à un problème de Dixmier concernant le cœur des idéaux premiers des algèbres enveloppantes 21/03/2005 14:30 001
+ Thomas AUBRIOT Classification des objets galoisiens de $U_q(\mathfrak{g})$ à homotopie près 14/03/2005 14:30 001
En se basant sur la vision des extensions de Hopf-Galois comme analogue non commutatif des fibrés principaux, nous redonnons la notion d'homotopie introduite par Kassel et développée par Kassel et Schneider. Nous considérons alors l'exemple des algèbres enveloppantes quantiques de Drinfeld-Jimbo $U_q(\mathfrak{g})$ pour voir comment cette notion d'homotopie permet une classification plus simple que celle à isomorphisme près : il est alors possible de construire un représentant explicite de chaque classe d'homotopie d'objets $U_q(\mathfrak{g})$-galoisiens par générateurs et relations. En fait, ces représentants sont des extensions clivées de $U_q(\mathfrak{g})$ et les cocycles correspondants sont obtenus à partir de cocycles sur les élements ``group like'' de $U_q(\mathfrak{g})$.
+ Baohua FU Résolutions symplectiques des singularités quotients 07/03/2005 14:30 001
On discutera la géométrie globale intrinsèque (à la correspondence de McKay) des résolutions symplectiques des singularités quotients.
+ Jean-Marie BOIS Corps enveloppants des algèbres de type Witt en caractéristique $0$ 28/02/2005 14:30 001
+ David HERNANDEZ Preuve de la conjecture de Kirillov-Reshetikhin pour les représentations des algèbres affines quantiques 21/02/2005 14:30 001
+ Bruno VALLETTE Dualité de Koszul des props 14/02/2005 14:30 001
La notion de prop modélise les opérations à plusieurs entrées et plusieurs sorties, agissant sur certaines structures algèbriques comme les bigèbres et les bigèbres de Lie. Nous montrons une théorie de dualité de Koszul pour les PROPs qui généralise celle des algèbres associatives et des opérades. Cette théorie de dualité de Koszul au niveau des props donne le modèle minimal pour les props de Koszul. Elle permet de définir des notions telles que celle de bigèbres de Lie à homotopie près. Enfin, elle permet de calculer l'homologie de certaines familles de graphes de Kontsevich.
+ Jie XIAO Derived Categories and Infinite Dimensional Lie Algebras 14/02/2005 16:00 001
+ Christof GEISS Some aspects of cluster mutation via preprojective algebras 31/01/2005 14:30 001
+ Julien MARCHÉ L'intégrale de Kontsevich des nœuds toriques 24/01/2005 14:30 001
+ Bernard LECLERC Modules de Verma et algèbres préprojectives 17/01/2005 14:30 001
+ David BESSIS Monoïdes de tresses et partitions non-croisées 03/01/2005 14:30 001
+ Koen De NAEGHEL On the classification of modules over elliptic algebras 13/12/2004 14:30 001
+ Bertrand TOËN Dg-catégories et espaces de modules associés 06/12/2004 14:30 001
Pour une dg-catégorie $T$, on s'intéresse à la construction d'un espace (ou plutôt d'un $n$-champ) de modules $Spel(T)$ classifiant les objets compacts de $T$. Sous des hypothèses de finitude sur $T$ (générateur compact, saturation...) on montre que le $n$-champ $Spel(T)$ est algébrique et localement de présentation finie. On peut aussi décrire ses sous-$n$-champs de présentation finie en imposant certaines bornes cohomologiques sur les objets de $T$. Finalement, la donnée d'un t-structure sur $T$, permet de construire un sous $1$-champ ouvert $Perv(T)$ dans $Spel(T)$ formé des objets pervers. On s'attend aussi à ce que la donnée d'une condition de stabilité à la Bridgeland permette de construire des sous champs propres dans $Perv(T)$. Lorsque $T$ est la dg-catégorie des complexes quasi-cohérents sur un schéma $X$, propre et lisse sur une base S, on obtient ainsi l'existence d'un $n$-champ algébrique des complexes parfaits d'amplitude $n-1$ sur $X$, ainsi qu'un champ algébrique (au sens usuel) des faisceaux pervers pour une t-structure donnée sur $D(X)$. Lors de cet exposé, je présenterai ces résultats d'un point de vue plutot informel, et mettrai en valeur les deux outils techniques essentiels que sont la théorie homotopique des dg-catégories, et la géométrie algébrique ``homotopique'' développée en collaboration avec G. Vezzosi.
+ Ualbai UMIRBAEV Tame and wild automorphisms of polynomial algebras and free associative algebras 29/11/2004 14:30 001
+ Michael BAROT Simply laced cluster algebras and unit forms 22/11/2004 14:30 001
+ Christian KRATTENTHALER Dénombrement des $\mathfrak{b}$-idéaux $ad$-nilpotents 15/11/2004 14:30 001
+ Igor BURBAN Sur la catégorie dérivée d'une courbe elliptique singulière 08/11/2004 14:30 001
+ Alexander ZIMMERMANN Dégénérescences dans les catégories dérivées 18/10/2004 14:30 001
+ Marcelo AGUIAR Hopf algebras related to symmetric functions 11/10/2004 14:30 001
+ Journée d'Algèbre en hommage à M.-P. MALLIAVIN 04/10/2004 14:30 001
+ Rosane USHIROBIRA Un théorème du type Amitsur-Levitzki pour les superalgèbres de Lie $osp(1,2n)$ 07/06/2004 14:30 001
+ Dmitri PANYUSHEV ad-nilpotent ideals of a Borel subalgebra : combinatorics, algebra, and geometry 17/05/2004 14:30 001
+ Olivier SCHIFFMANN Bases canoniques des algèbres de lacets via les schémas Quot 10/05/2004 14:30 001
+ Maxim NAZAROV Rational representations of Yangians associated with skew Young diagrams 03/05/2004 14:30 001
+ Amnon YEKUTIELI Grothendieck Duality via Rigid Dualizing Complexes and Differential Graded Algebras 03/05/2004 15:45 001
+ Jerzy WEYMAN Geometric method of calculating syzygies 26/04/2004 14:30 001
+ Alexei BONDAL $T$-structures and stability conditions in triangulated categories 22/03/2004 14:30 001
+ Lionel RICHARD Isomorphisme entre des algèbres de Weyl généralisées quantiques 15/03/2004 14:30 001
+ Rupert YU Indice des algèbres de Lie de type ``seaweed'' 08/03/2004 14:30 001
+ Frédéric CHAPOTON Carquois avec relations associés aux clusters 01/03/2004 14:30 001
+ Xiuping SU Tame roots of wild quivers 23/02/2004 14:30 001
+ Charles TOROSSIAN Quantification, Espaces symétriques et fonction E(x,y) de Rouvière 16/02/2004 14:30 001
+ Anton ALEKSEEV The non-commutative Chern-Weil homomorphism 09/02/2004 14:30 001
+ Nicolas MARCONNET Dualité de Poincaré pour les algèbres homogènes 02/02/2004 14:30 001
+ Olivier SCHIFFMANN Actions de groupes de tresse et de Weyl et variétés carquois 26/01/2004 14:30 001
+ Alexander ODESSKII Bi-hamiltonian structures and commuting elements in elliptic algebras 19/01/2004 14:30 001
+ Bangming DENG Generic extensions and canonical bases for cyclic quivers 12/01/2004 14:30 001
+ Grégory GINOT Représentation des star-produits pour des sous-variétés co-isotropes 15/12/2003 14:30 001
+ D. JORDAN Noetherian rings, localisation and Eulerian derivatives 08/12/2003 14:30 001
+ Wendy LOWEN Deformations of abelian categories 01/12/2003 14:30 001
+ David HERNANDEZ Etude algébrique des q,t-caractères de Nakajima : racines de l'unité et au-delà du cas fini 17/11/2003 14:30 001
+ Igor BURBAN Derived tameness of the degenerate tubular algebra 10/11/2003 14:30 001
+ Ivan MARIN Sur les représentations du groupe de tresses 03/11/2003 14:30 001
+ Bertram KOSTANT Powers of the Euler product and commutative subalgebras of complex simple Lie algebras 20/10/2003 14:30 001
+ Alexander PREMET The representation pattern associated with the minimal nilpotent orbit 13/10/2003 14:30 001
+ Dmitri PANYUSHEV On generators and duality for ad-nilpotent ideals 16/06/2003 14:30 001
+ Friedrich KNOP On Noether's and Weyl's bound in positive characteristic 16/06/2003 15:45 001
+ F. van OYSTAEYEN From non commutative geometry to functions of non commuting variables 02/06/2003 14:30 001
+ Alexander PREMET Nilpotent commuting varieties of reductive Lie algebras and punctual Hilbert schemes 26/05/2003 14:30 001
+ Ivan ARZHANTSEV Affine embeddings of homogeneous spaces and invariant subalgebras 19/05/2003 14:30 001
+ Michel van den Bergh Quasi-invariants for complex reflection groups 05/05/2003 14:30 001
+ Tatiana GATEVA-IVANOVA A combinatorial approach to the set-theoretic solutions of the Yang-Baxter equation 28/04/2003 14:30 001
+ François DUMAS Automorphismes de $U^+_q(g)$ 31/03/2003 14:30 001
+ Matthieu PICANTIN Monoïdes duaux pour les groupes d'Artin-Tits sphériques 24/03/2003 14:30 001
+ Alain TROESCH Algèbre homologique dans des catégories de foncteurs 17/03/2003 14:30 001
+ Laurent MANIVEL Une occurrence géométrique de la trialité de Cartan 10/03/2003 14:30 001
+ Bernhard KELLER Sur la construction de Lyubashenko de la $A_\infty$-catégorie des $A_\infty$-foncteurs 03/03/2003 14:30 001
+ Benjamin ENRIQUEZ Sur les foncteurs de quantifications de bigèbres de Lie 24/02/2003 14:30 001
+ Emanuela PETRACCI Les invariants de Gorelik 17/02/2003 14:30 001
+ Pascal LAVAUD Superpfaffien 03/02/2003 14:30 001
+ Laurent RIGAL Algèbres quantiques avec loi de redressement 27/01/2003 14:30 001
+ Matthias MEULIEN Sur les invariants des pinceaux de quintiques binaires 20/01/2003 14:30 001
+ Olivier SCHIFFMANN Réalisation homologique de variétés de Nakajima et actions du groupe de Weyl 13/01/2003 14:30 001
+ Cyril GRUNSPAN Torseur quantiques 06/01/2003 14:30 001
+ Anthony JOSEPH Le semi-centre de l'algèbre enveloppante d'un parabolique de $sl(n)$ 16/12/2002 14:30 001
+ Nicolás ANDRUSKIEWITSCH Des épaves aux algèbres de Hopf pointées 02/12/2002 14:30 001
+ Alexander ODESSKII et-theoretical solutions to the Yang-Baxter Relation from factorization of matrix polynomials and theta-functions 11/11/2002 14:30 001
+ Yuriy DROZD Catégories dérivées des faisceaux cohérents sur quelques courbes projectives 04/11/2002 14:30 001
+ Karin ERDMANN Hecke algebras of symmetric groups and varieties of modules 28/10/2002 14:30 001
+ V. DLAB Homological duality 21/10/2002 14:30 001
+ Alexis TCHOUDJEM Cohomologie des fibrés en droites sur la compactification magnifique d'un groupe semi-simple adjoint 14/10/2002 14:30 001
+ Gérard CAUCHON Effacement des dérivations; applications aux algèbres quantiques 07/10/2002 14:30 001
+ Earl TAFT Suites récurrentes et identités combinatoires 24/06/2002 14:30
+ Loïc FOISSY Algèbres de Hopf d'arbres enracinés et renormalisation 27/05/2002 14:30
+ Caroline GRUSON Cône nilpotent impair de certaines super algèbres de Lie 27/05/2002 15:45
+ Caroline GRUSON Cône nilpotent impair de certaines super algèbres de Lie 13/05/2002 14:30
+ Amnon NEEMAN On the work of Ben Martin towards a generalised Casson invariant 06/05/2002 14:30
+ Markus REINEKE Cohomology of quiver moduli 08/04/2002 14:30
+ Alexei BONDAL Generators in triangulated categories 25/03/2002 14:30
+ Gilles HALBOUT Une version déformée du théorème de Kontsevich 18/03/2002 14:30
+ Klaus BONGARTZ Orbit closures of finite-dimensional modules 18/03/2002 15:45
+ Alberto CATTANEO Poisson manifolds and symplectic groupoids 11/03/2002 14:30
+ Hans-Jürgen SCHNEIDER A characterization of quantum groups 04/03/2002 14:30
+ Alfons OOMS Commutative polarizations in Lie algebras 25/02/2002 14:30
+ Benoit FRESSE Autour de l'opérade de Barratt-Eccles et des cochaînes de Hochschild 18/02/2002 14:30
+ M. VIGUÉ Caractérisation de la structure produit d'une algèbre à l'aide de l'homologie de Hochschild 11/02/2002 14:30
+ Alexander ZIMMERMANN Algèbres gentilles et équivalences dérivées 04/02/2002 14:30
+ Michel van den Bergh Non-commutative quadrics 28/01/2002 14:30
+ Sonia NATALE On the classification of semisimple Hopf algebras 21/01/2002 14:30
+ Wilberd van DER KALLEN Towards a cohomological invariant theory 21/01/2002 15:45
+ Philippe CALDERO Propriétés multiplicatives des mineurs quantiques drapeaux 14/01/2002 14:30
+ Shmuel ZELIKSON Carquois d'Auslander-Reiten et tableaux de Young 07/01/2002 14:30
+ Christof GEISS Algebras with non reduced automorphism groups 10/12/2001 14:30
+ Nicolás ANDRUSKIEWITSCH Triangular Hopf algebras with the Chevalley property 03/12/2001 14:30
+ Alexander PANOV Quantum solvable algebras 26/11/2001 14:30
+ Olivier MATHIEU Endomorphismes du module de Steinberg pour les groupes de lacets 19/11/2001 14:30
+ Francis SERGERAERT Un cas d'algèbre expérimentale 12/11/2001 14:30
+ Charles TOROSSIAN Application de la quantification de Kontsevich à la conjecture de Kashiwara-Vergne 05/11/2001 14:30
+ Alexander ODESSKII Elliptic algebras 29/10/2001 14:30
+ Bernhard KELLER Groupes d'automorphismes d'extensions centrales (d'après M. Saorín) 15/10/2001 14:30
+ Maxim NAZAROV Induced representations of affine Hecke algebras and canonical bases of quantum groups 11/06/2001 14:30
+ Vladimir RUBTSOV Quasi-Hopf algebras associated with sl2 and complex curves 28/05/2001 14:30
+ Lieven LE BRUYN How to find braid group representations ? 21/05/2001 14:30
+ Michel van den Bergh Counting representations over finite fields and quiver varieties 07/05/2001 14:30
+ Raf BOCKLANDT Coregular quiver representations 26/03/2001 14:30
+ Christian KASSEL Surjectivité de la norme pour l'action d'un groupe cyclique sur un anneau 19/03/2001 14:30
+ Henrik THYS $R$-matrices pour la quantification de la superalgèbre de Lie $D(2,1,x)$ et un invariant de noeuds associé 12/03/2001 14:30
+ Gilles HALBOUT Déformation et réduction coisotrope 05/03/2001 14:30
+ Marc ROSSO Groupes quantiques et combinatoire des mots 26/02/2001 14:30
+ Benjamin ENRIQUEZ Quantification des bigèbres de Lie et algèbres de battages 19/02/2001 14:30
+ Bertrand PATUREAU-MIRAND Superalgèbres de Lie et invariants de noeuds 12/02/2001 14:30
+ Bangming DENG Hall algebras and Lusztig's symmetries 05/02/2001 14:30
+ Johannes HUEBSCHMANN Algèbres de Lie-Rinehart et algèbres de Batalin-Vilkovisky 29/01/2001 14:30
+ Frédéric CHAPOTON Théorème de Milnor-Moore dendriforme et algèbres braces 22/01/2001 14:30
+ Jérôme GERMONI Sur la classification des représentations admissibles de l'algèbre de Virasoro 08/01/2001 14:30
+ Dmitri PANYUSHEV Isotropy representations, eigenvalues of a Casimir element, and commutative Lie algebras 18/12/2000 14:30
+ Roland BERGER Koszulité pour les algèbres homogènes non quadratiques 11/12/2000 14:30
+ Christof GEISS Horn's problem and semi-stability for representations of quivers 04/12/2000 14:30
+ Philippe CALDERO Paramétrisation de Lusztig de la base canonique et dégénérescence de variétés de drapeaux 27/11/2000 14:30
+ Thomas BRÜSTLE Derived tameness, quadratic forms and elliptic Lie algebras 20/11/2000 14:30
+ Rupert YU Description explicite des centralisateurs de paires nilpotentes distinguées dans les algèbres de Lie classiques 13/11/2000 14:30
+ Pierre BAUMANN Bases canoniques et un théorème de R. W. Richardson 06/11/2000 14:30
+ Amnon NEEMAN Strange abelian categories 30/10/2000 14:30
+ Sophie CHEMLA L'image inverse pour les algébroïdes de Lie 23/10/2000 14:30
+ Earl TAFT Les structures de bigèbres de Lie sur les algèbres de Witt et de Virasoro 09/06/2000 09:30
+ Theodora THEOHARI-APOSTOLIDI Graded algebras, crossed products and Auslander-Reiten sequences 05/06/2000 14:30
+ Athanassios PAPISTAS Lie algebras and fixed points 05/06/2000 16:00
+ Paul SEIDEL ntroduction aux catégories de Fukaya 29/05/2000 14:30
+ Jan SCHRÖER The variety of pairs of nilpotent matrices annihilating each other 15/05/2000 14:30
+ Juan CUADRA The Brauer Group of a Hopf Algebra 27/03/2000 14:30
+ Alberto ARABIA Relèvement des algèbres lisses et de leurs morphismes 20/03/2000 14:30
+ Caroline GRUSON Cohomologie des superalgèbres de Lie et variété autocommutante 13/03/2000 14:30
+ Olivier MATHIEU Sur la classification des algèbres de Lie simples en caractéristique $p$ 06/03/2000 14:30
+ Séverine LEIDWANGER Les différentes réalisations de la représentation basique de $A_{(n-1)}^{(1)}$ et la combinatoire des partitions 28/02/2000 14:30
+ Stéphanie CUPIT-FOUTOU Classification des Variétés-à-deux-orbites 14/02/2000 14:30
+ Steffen KÖNIG Schur-Weyl duality and dominant dimension 07/02/2000 14:30
+ Raphaël ROUQUIER Invariance des automorphismes extérieurs par équivalences stables ou dérivées 31/01/2000 14:30
+ Frédéric CHAPOTON Permutoèdres, associaèdres et leurs algèbres de Hopf 24/01/2000 14:30
+ Alain GUICHARDET Homologie et cohomologie du tore quantique multiparamétré 17/01/2000 14:30
+ Alexander ZIMMERMANN Action des automorphismes d'un groupe sur sa cohomologie 10/01/2000 14:30
+ I. GORDON Modular representations of Lie algebras and quantum groups 13/12/1999 14:30
+ R. FARNSTEINER Rank varieties, schemes of tori, and the representation type of infinitesimal groups 06/12/1999 14:30
+ Laurent RIGAL Le premier théorème fondamental de la théorie des coinvariants pour le groupe quantique $O_q(GL_t)$ 29/11/1999 14:30
+ Thierry LEVASSEUR Opérateurs différentiels sur certaines orbites nilpotentes 15/11/1999 14:30
+ Matthias KÜNZER Ties for the integral group algebra of the symmetric group 08/11/1999 14:30
+ Shmuel ZELIKSON Multiplicités des filtrations de Brylinski-Kostant 25/10/1999 14:30
+ Peter LITTELMANN Drapeaux tordus de modules de Verma et bases pour les représentations irréductibles 18/10/1999 14:30
+ Andrzej SKOWRONSKI The algebras of semi-invariants of quivers 11/10/1999 14:30
+ Victor KAC Commuting triples in compact Lie groups 07/06/1999 14:30
+ Lieven LE BRUYN Formal non-commutative structures 31/05/1999 14:30
+ Yuriy DROZD Les noeuds non-commutatifs et leurs catégories dérivées 17/05/1999 14:30
+ Nicole SNASHALL Hochschild cohomology of finite-dimensional algebras 10/05/1999 14:30
+ Alain VERSCHOREN Invariants involutifs de domains de Krull 03/05/1999 14:30
+ Corrado De CONCINI Cohomology of Coxeter and Artin groups 12/04/1999 14:30
+ F. HIVERT Formules de Weyl et Demazure pour un groupe quantique dégénéré 29/03/1999 14:30
+ A. SOLOTAR Sur le théorème de Hochschild-Kostant-Rosenberg pour les cogèbres 22/03/1999 14:30
+ Benoit FRESSE Homologie de Poisson de surfaces à une singularité isolée 08/03/1999 14:30
+ Dmitri PANYUSHEV Nilpotent pairs, dual pairs, and sheets 22/02/1999 14:30
+ F. COELHO Algebras of small homological dimension 15/02/1999 14:30
+ Leonid VAINERMAN Les structures quantiques et les inclusions de facteurs de von Neumann 08/02/1999 14:30
+ Ken GOODEARL Direct sum decomposition problems over von Neumann regular rings 01/02/1999 14:30
+ Ken GOODEARL Quantum determinantal ideals 25/01/1999 14:30
+ Ken GOODEARL Quantized primitive spectra as quotients of affine varieties 18/01/1999 14:30
+ Ken GOODEARL Stratified prime spectra in quantum coordinate rings 11/01/1999 14:30
+ E. LANZMANN Le théorème d'annulation pour la super-algèbre de Lie $osp(1,2l)$ 14/12/1998 14:30
+ Gerhard RÖHRLE Actions of parabolic groups and quasihereditary algebras II 07/12/1998 14:30
+ Thomas BRÜSTLE Actions of parabolic groups and quasihereditary algebras 30/11/1998 14:30
+ Alberto TONOLO Tilting modules and Quasi-Tilting Modules 23/11/1998 14:30
+ Tom LENAGAN Poincaré series of multifiltered algebras 16/11/1998 14:30
+ M. SAORIN On automorphism groups induced by bimodules 09/11/1998 14:30
+ Michel van den Bergh Abstract blowing down 19/10/1998 14:30
+ Markus REINEKE Bases for degenerate quantum groups 19/10/1998 16:00
+ Walter BORHO On relations of completely prime primitive ideals to adjoint orbits 12/10/1998 14:30
+ Daya-Nand VERMA Orbit method and algebraic groups 05/10/1998 14:30
+ D. VOIGT Representation theory of finite algebraic groups 08/06/1998 14:30
+ J. GOMEZ-TORRECILLAS Multi-filtered algebras and modules 25/05/1998 14:30
+ Yuriy DROZD La classification des Z-modules quadratiques 18/05/1998 14:30
+ F. van OYSTAEYEN Noncommutative schemes 11/05/1998 14:30
+ Peter DRÄEXLER Classes of tame algebras associated with tubes 04/05/1998 14:30
+ A. A. MIKHALEV Groupe de Grothendieck et caractère de Chern pour une quantification d'une surface de Klein 27/04/1998 14:30
+ Alain BRUGUIÈRES Catégories prémodulaires, modularisation et invariants de variétés de dimension 3 06/04/1998 14:30
+ P. SMITH Non-commutative surfaces III 23/03/1998 14:30
+ P. SMITH Non-commutative surfaces II 16/03/1998 14:30
+ P. SMITH Non-commutative surfaces I 09/03/1998 14:30
+ M. SCHMIDMEIER Kronecker's problem for semilinear maps 02/03/1998 14:30
+ Alexander ZIMMERMANN Le groupe d'auto-équivalences de la catégorie dérivée d'une algèbre 23/02/1998 14:30
+ U. OBERST A Duality Theorem for Modules over a Variant of the One-Dimensional Weyl algebra. Applications to Time-Varying Linear Systems and Algorithms 16/02/1998 14:30
+ Shmuel ZELIKSON ur les polynômes de saut de R. K. Brylinski 09/02/1998 14:30
+ M. VIGUÉ Sur la structure d'algèbre de l'homologie de Hochschild 26/01/1998 14:30
+ C. OHN $SL(3)$ quantiques et représentations 19/01/1998 14:30
+ H. LI Some applications of Groebner bases 15/12/1997 14:30
+ Thierry LEVASSEUR Champs de vecteurs sur l'espace tangent d'un espace symétrique semi-simple 08/12/1997 14:30
+ Eduardo MARCOS Hochschild cohomology of truncated quiver algebras 01/12/1997 14:30
+ Georges PAPADOPOULO Formule de caractère pour une famille stable de représentations modulaires simples de $GL_n$ (en collaboration avec O. Mathieu) 24/11/1997 14:30
+ O. FLEURY Sous-groupes finis de $Aut(U(sl_2))$ 17/11/1997 14:30
+ Roland BERGER Confluence et Koszulité 03/11/1997 14:30
+ Thomas BRÜSTLE On the orbits of parabolics on their unipotent radical 27/10/1997 14:30
+ K. van ROMPAY Some quantum P3's with finitely many points 20/10/1997 14:30
+ A. EL ALAOUI La table des caractères pour une algèbre de Hopf 16/06/1997 14:30
+ M. DIJKHUIZEN Covariant Poisson brackets on symmetric spaces and their quantization 09/06/1997 14:30
+ P. FLEISCHMANN On constructive modular invariant theory of finite groups 02/06/1997 14:30
+ V. DLAB Stratified algebras 26/05/1997 14:30
+ Eric OPDAM On the spectral decomposition of the affine Hecke algebra 12/05/1997 14:30
+ R. ABBYANKAR Semilinear Transformations 05/05/1997 14:30
+ Rosane USHIROBIRA Sur la méthode des orbites pour les algèbres de champs de vecteurs sur une courbe 28/04/1997 14:30
+ Stefaan CAENEPEEL Making the category of Doi-Hopf modules into a braided monoidal category 21/04/1997 14:30
+ Vladimir BAVULA Filter Dimension and its Application to simple affine Algebras 24/03/1997 14:30
+ Rupert YU Polytopes associés aux représentations de $sl(n)$ 17/03/1997 14:30
+ Victor PETROGRADSKY On growth in Lie algebras, generalized partitions and analytic functions 10/03/1997 14:30
+ Pascual JARA Locally finite modules over noetherian rings 03/03/1997 14:30
+ William FULTON Quantum cohomology and Schubert polynomials 24/02/1997 14:30
+ Claude CIBILS Anneaux de Grothendieck de groupes quantiques basiques aux racines de l'unité 17/02/1997 14:30
+ Thierry LAMBRE Le caractère de Chern en homologie cyclique : exemples 10/02/1997 14:30
+ Dirk KUSSIN Graded Factorial Algebras, Quaternions and Preprojective Algebras 03/02/1997 14:30
+ W. LEMPKEN Generalizations of Frobenius Groups 27/01/1997 14:30
+ D. JORDAN Graded rings generated by $q$-difference operators 20/01/1997 14:30
+ O. FLEURY Automorphismes de $U_q(b^+)$ 13/01/1997 14:30
+ O. SOLBERG Exact categories in the representation theory of artin algebras 16/12/1996 14:30
+ Alexander ROSENBERG Beilinson-Bernstein Localization Construction for quantized enveloping Algebras. $D$-modules on non commutative Schemes 09/12/1996 14:30
+ Alexander ROSENBERG $D$-calculus and differential Operators on non commutative Spaces 02/12/1996 14:30
+ Philippe CALDERO Projecteurs pour l'action d'une algèbre de Lie nilpotente et applications 25/11/1996 14:30
+ Alexander ROSENBERG Multiparametric Quantum Groups 18/11/1996 14:30
+ Alexander ROSENBERG Reconstruction of Schemes 04/11/1996 14:30
+ Laurent RIGAL Inégalité de Bernstein pour l'algèbre de Weyl quantique 28/10/1996 14:30
+ A. A. MIKHALEV Canonical basis in Lie Super Algebras 21/10/1996 14:30
+ Alexander ROSENBERG Non Commutative Algebraic Geometry 14/10/1996 14:30