Equipe(s)  Responsable(s)  Salle  Adresse 

Analyse Algébrique Topologie et Géométrie Algébrique 
Penka Georgieva, Elba GarciaFailde, Ilia Itenberg, Alessandro Chiodo 
1516  413  Jussieu 
Orateur(s)  Titre  Date  Début  Salle  Adresse  

+  Kento Osuga  Refined correspondence between Hurwitz numbers and topological recursion  22/09/2023  14:00  1516413  Jussieu  
It has been proven that one can construct generating functions of Hurwitz numbers from topological recursion on an appropriate spectral curve. In this talk, I will explore this correspondence in a refined setting. On one hand, we have enumerative invariants of maps onto possibly nonorientable surfaces, and on the other hand, we have refined topological recursion on a refined spectral curve. After reviewing both aspects, I will give a sketch of how to prove their correspondence. If time permits, I will mention how far we can extend, and also mention other applications of the refined topological recursion. This talk is partly based on work in progress with Nitin Chidambaram and Maciej Dolega. 

+  Guangbo Xu  Arnold conjecture over Z  16/06/2023  15:00  1516413  Jussieu  
Arnold's conjecture on the numbers of fixed points of Hamiltonian diffeomorphisms on symplectic manifolds has motivated numerous important developments in geometry and topology, most notably the invention of Floer homology. In this talk I will present the recent proof of the integral version of the Arnold conjecture: on any closed symplectic manifold, the number of fixed points of a nondegenerate Hamiltonian diffeomorphism is bounded from below by a version of total Betti number over Z, which takes accounts of torsions of all characteristics. This result strengthens the rational version proved by FukayaOno and LiuTian as well as the finite field version proved recently by AbouzaidBlumberg. The most crucial inputs of the proof are 1) FukayaOno's idea of integral counting of holomorphic curves, the detail of which has been worked out recently by a previous joint work with Shaoyun Bai, and 2) the construction of global Kuranishi charts for the Hamiltonian Floer flow category which generalizes the recent work of AbouzaidMcLeanSmith. This talk is based on the joint work with Shaoyun Bai (arxiv: 2209.08599). 

+  Boris Bychkov  Topological recursion for generalized double Hurwitz numbers  21/04/2023  14:00  1516413  Jussieu  
Topological recursion is a remarkable universal recursive procedure that has been found in many enumerative geometry problems, from combinatorics of maps, to random matrices, GromovWitten invariants, Hurwitz numbers, Mirzakhani's hyperbolic volumes of moduli spaces, knot polynomials. A recursion needs an initial data: a spectral curve, and the recursion defines the sequence of invariants of that spectral curve. In the talk I will define the topological recursion, spectral curves and their invariants, and illustrate it with examples; I will introduce the Fock space formalism which proved to be very efficient for computing TRinvariants for the various classes of Hurwitztype numbers and I will describe our results on explicit closed algebraic formulas for generating functions of generalized double Hurwitz numbers, and how this allows to prove topological recursion for a wide class of problems. If time permits I'll talk about the implications for the socalled ELSVtype formulas (relating Hurwitztype numbers to intersection numbers on the moduli spaces of algebraic curves). The talk is based on the series of joint works with P. DuninBarkowski, M. Kazarian and S. Shadrin. 

+  Renzo Cavalieri  A log/tropical take on Hurwitz numbers  14/04/2023  14:00  1516413  Jussieu  
I will present some recent joint work with Hannah Markwig and Dhruv Ranganathan, in which we interpret double Hurwitz numbers as intersection numbers of the double ramification cycle with a logarithmic boundary class on the moduli space of curves. This approach removes the "need" for a branch morphism and therefore allows the generalization to related enumerative problems on moduli spaces of pluricanonical divisors  which have a natural combinatorial structure coming from their tropical interpretation. 

+  Charles Arnal  Recursively patchworking real algebraic hypersurfaces with asymptotically large Betti numbers  07/04/2023  14:00  1516413  Jussieu  
I will present a new technique that builds on previous work by O. Viro and I. Itenberg and allows one to effortlessly define families of real projective algebraic hypersurfaces using alreadydefined families in lower dimensions as building blocks. The asymptotic (in the degree) Betti numbers of the real parts of the resulting families can then be recovered from the asymptotic Betti numbers of the real parts of the building blocks. Using this technique, I will explain how families of real algebraic hypersurfaces whose real parts have asymptotically large Betti numbers can be constructed in any dimension. 

+  Gleb Koshevoy  Maximal green sequences for triangle products  31/03/2023  14:00  1516413  Jussieu  
The existence of maximal green sequences is an important property of a cluster algebra. We construct explicit maximal green sequences for triangle products of an acylic quiver with a Dynkin quiver. As an application we deduce from the work of GrossHackingKeelKontsevich the full FockGoncharov conjecture for big double Bruhat cells for simplyconnected, connected, semisimple groups of simplylaced type. Maximal green sequences are also useful for computing DonaldsonThomas invariants and transformations. We compute normalized DTinvariants for triangle products of Dynkin quivers. For products of the Dynkin quivers, the DTtransformations are related to the RobinsonSchenstedKnuth bijection. The talk is based on joint work with V.Genz and work in progress with T.Scrimshaw. 

+  Amanda Hirschi  Global Kuranishi charts for moduli spaces in symplectic GW theory  24/03/2023  14:00  1516413  Jussieu  
I will explain the construction of a global Kuranishi chart for moduli spaces of pseudoholomorphic stable maps and show how this allows for a straightforward definition of symplectic GW invariants. Afterwards, I will outline how global Kuranishi charts can be used to prove a product formula for GW invariants and, if time permits, describe a virtual localisation result in the vein of the analogous result by GraberPandharipande. 

+  Nathan Priddis  BHK mirror symmetry  17/03/2023  14:00  1516413  Jussieu  
Almost 30 years ago, Berglund and Hübsch proposed a version of Mirror Symmetry for quasihomogeneous potentials, which was later completed by Krawitz. To a LandauGinzburg pair (W,G) of a potential W and a group of symmetries G, we can relate its BHK mirror (W‘,G‘) by a simple rule. In this presentation, we will discuss BHK mirror symmetry, its relation with other forms of mirror symmetry, and an extension of BHK mirror symmetry to nonabelian groups. 

+  Paolo Gregori  Resurgence and large genus asymptotics of intersection numbers  10/03/2023  14:00  1516411  Jussieu  
In this talk, I will present a new approach to the computation of the large genus asymptotics of intersection numbers of psiclasses, Thetaclasses, and of rspin intersection numbers. This technique is based on a resurgent analysis of the generating functions of such intersection numbers, which are computed via determinantal formulae, and relies heavily on the presence of an underlying first order differential system for each of the problems taken into consideration. With this approach we are able to extend the results of Aggarwal (2021) with the computation of subleading corrections, and to obtain completely new results on rspin and Thetaclass intersection numbers. 

+  Thomas Blomme  Invariants raffinés et polynomialité  27/01/2023  14:00  1516413  Jussieu  
Dans le plan projectif complexe, il est possible de compter les courbes de degré et genre fixé passant par un nombre de points convenable pour obtenir un nombre qui s’avère ne pas dépendre du choix des points. En géométrie tropicale, I. Itenberg et G. Mikhalkin ont montré qu’il est possible de compter les courbes tropicales solutions du problème analogue avec des multiplicités polynomiales de sorte que le compte polynomial obtenu soit également invariant. Dans cet exposé on s’intéressera à des généralisations de ces invariants polynomiaux dans d’autre surfaces, leur calcul ainsi les propriétés de régularité qui en découlent. 

+  Paolo Rossi  Meromorphic differentials and integrable hierarchies  20/01/2023  14:00  1516413  Jussieu  
On the complex projective line, for any configuration of n distinct marked points and n integers whose sum is 2, there is a meromorphic differential, unique up to rescaling, whose zeros and poles coincide with those marked points and have order prescribed by the integers. Working up to the complex 3dimensional group of projective transformations, this means that the number of meromorphic differentials with prescribed order of zeros and poles is finite if and only if n=3. Since the sum of the orders needs two be 2, only two cases are left: two zeros and one pole or two poles and one zero. These numbers of differentials can be enriched by allowing extra poles, but with the constraint that their residue vanishes. Problem: compute these two families of integer numbers. In joint works with A. Buryak and D. Zvonkine we provide the answer to this problem and a certain higher genus generalization, together with and intriguing relation to integrable systems. 

+  John Alexander Cruz Morales  An approach to Dubrovin conjecture from GLSM point of view  13/01/2023  15:00  1516413  Jussieu  
In this talk I will review part of an ongoing project aiming to understand Dubrovin conjecture from the perspective of Gauged Linear Sigma Models (GLSM). One important part of the Dubrovin conjecture relates the geometry of the (bounded) derived category of coherent sheaves of a Fano manifold X and the asymptotic behaviour of its quantum differential equation around infinity. I will explain the role of the hemisphere partition function introduced by Hori and Romo in this story by analysing one simple (but non trivial) case, namely: the CP^{k1}model. If time permits, I will also discuss the CP^{k1}model with twisted masses (equivariant model). This is a joint work with Jin Chen and Mauricio Romo. 

+  Pierre Descombes  DonaldsonThomas theory of local CalabiYau threefolds  12/12/2022  11:00  1516413  Jussieu  
DonaldsonThomas (DT) theory is a modern branch of enumerative and algebraic geometry, taking inspiration from string theory, aiming at counting sheaves on calabiyau threefolds. I will expose some recent progress on DT theory on crepant resolutions of CalabiYau singularities. 

+  Denis Auroux  Fonctions analytiques et homologie de Floer pour les surfaces de Riemann et leurs miroirs  09/12/2022  14:00  1516413  Jussieu  
Cet exposé concerne la symétrie miroir homologique pour les surfaces de Riemann. Après des exemples élémentaires (cylindre et pantalon), on considérera les décompositions le long de cylindres (thèse de Heather Lee) pour arriver à un résultat de symétrie miroir général. On verra en particulier le lien entre les trajectoires de Floer dans les portions cylindriques d'une surface et les développements en série de Laurent des fonctions analytiques sur le miroir. On esquissera enfin une description des catégories de Fukaya de surfaces singulières que l'on peut considérer comme les miroirs de surfaces de Riemann (travail en collaboration avec Efimov et Katzarkov). 

+  Adrien Sauvaget  On spin GW/Hurwitz correspondence  02/12/2022  14:00  1516413  Jussieu  
Spin GW invariants were introduced by Kiem and Li to determine the GW invariants of surfaces with smooth anticanonical divisors. This numbers are conjectured to be equal to linear combinations of Spin Hurwitz numbers which can be computed via representation theory: this is the socalled spin GW/Hurwitz correspondence. I will explain that this conjecture is valid if the target is P^1 and in general if we assume a general structure of spin GW invariants. 

+  Grigory Mikhalkin  Enumeration of curves in ellipsoid cobordisms  25/11/2022  14:00  1516413  Jussieu  
Ellipsoid cobordisms are special case of toric surfaces. They correspond to quadrilaterals cut from the positive quadrants by two disjoint intervals. Holomorphic curves inside these cobordisms obstruct squeezing of one ellipsoid into another. We fit tropical curves into the socalled SFTframework, and observe a jumping phenomenon in the resulting enumeration. Based on the joint work with Kyler Siegel. 

+  Gabriele Rembado  Local wild mapping class group  18/11/2022  14:00  1525101  Jussieu  
The standard mapping class groups are fundamental groups of moduli spaces/stacks of pointed Riemann surfaces. The monodromy properties of 

+  Alex Degtyarev  Lines generate the Picard group of a Fermat surface  07/11/2022  11:00  1516413  Jussieu  
In 1981, Tetsuji Shioda proved that, for each integer m > 0 prime to 6, the 3m^2 lines contained in the Fermat surface \Phi_m: z_0^m+z_1^m+z_2^m+z_3^m=0 generate the Picard group of the surface over Q, and he conjectured that the same lines also generate the Picard group over Z. If true, this conjecture would give us a complete understanding of the NéronSeveri lattice of \Phi_m, leading to the computation of a number of more subtle arithmetical invariants. It was not until 2010 that the first numeric evidence substantiating the conjecture was obtained by Schütt, Shioda, and van Luijk and, in similar but slightly different settings, by Shimada and Takahashi. I will discuss a very simple purely topological proof of Shioda's conjecture and try to extend it to the more general socalled Delsarte surfaces, where the statement is not always true, raising a new open question.
If time permits, I will also discuss a few advances towards the generalization of the conjecture to the (2d+1)!! m^{d+1} projective dspaces contained in the Fermat variety of degree m and dimension 2d; this part is joint with Ichiro Shimada. 

+  Tyler Kelly  Open Mirror Symmetry for LandauGinzburg models  21/10/2022  14:00  1516413  Jussieu  
A LandauGinzburg (LG) model is a triplet of data (X, W, G) consisting of a regular function W:X → C from a quasiprojective variety X with a group G acting on X leaving W invariant. An enumerative theory developed by Fan, Jarvis, and Ruan inspired by ideas of Witten gives FJRW invariants, the analogue of GromovWitten invariants for LG models. These invariants are now called FJRW invariants. We define a new open enumerative theory for certain LandauGinzburg models. Roughly speaking, this involves computing specific integrals on certain moduli of disks with boundary and interior marked points. One can then construct a mirror LandauGinzburg model to a LandauGinzburg model using these invariants. If time permits or as interest of the audience guides, I will explain some key features that this enumerative geometry enjoys (e.g., topological recursion relations and wallcrossing phenomena). This is joint work with Mark Gross and Ran Tessler. 

+  Maria Yakerson  On the cohomology of Quot schemes of infinite affine space  14/10/2022  14:00  1516413  Jussieu  
Hilbert schemes of smooth surfaces and, more generally, their Quot schemes are wellstudied objects, however not much is known for higher dimensional varieties. In this talk, we will speak about the topology of Quot schemes of affine spaces. In particular, we will compute the homotopy type of certain Quot schemes of the infinite affine space, as predicted by Rahul Pandharipande. This is joint work in progress with Joachim Jelisiejew and Denis Nardin. 

+  Ellena Moskovsky  Generalising Narayana polynomials using topological recursion  30/09/2022  14:00  1516413  Jussieu  
Narayana polynomials arise in a number of combinatorial settings and have been proven to satisfy many properties, including symmetry, realrootedness and interlacing of roots. Topological recursion, on the other hand, is a unifying mathematical framework that has been proven to govern a vast breadth of problems. One relatively unexplored feature of topological recursion is its ability to generalise existing combinatorial problems; one can use this feature of topological recursion to motivate a particular generalisation of Narayana polynomials. In ongoing workinprogress with Norman Do and Xavier Coulter, we prove that the resultant generalised polynomials satisfy certain recursive and symmetry properties analogous to their original counterparts, while conjecturing that they also satisfy realrootedness and interlacing. 

+  Kendric Schefers  Microlocal perspective on homology  26/09/2022  14:00  1516413  Jussieu  
The difference between the homology and singular cohomology of a space can be seen as a measure of the singularity of that space. This difference as a measure of singularity can be made precise in the case of the special fiber of a map between smooth schemes by introducing the socalled "microlocal homology" of such a map, an object which records the singularities of the special fiber as well as the codirections in which they arise. In this talk, we show that the microlocal homology is in fact intrinsic to the special fiber—independent of its particular presentation by any map—by relating it to an object of 1shifted symplectic geometry: the canonical sheaf categorifying DonaldsonThomas invariants introduced by Joyce et al. Time permitting, we will discuss applications of our result to ongoing work relating to the singular support theory of coherent sheaves.


+  Xiaohan Yan  Quantum Ktheory of flag varieties via nonabelian localization  23/09/2022  14:00  1516413  Jussieu  
Quantum cohomology may be generalized to Ktheoretic settings by studying the "Ktheoretic analogue" of GromovWitten invariants defined as holomorphic Euler characteristics of sheaves on the moduli space of stable maps. Generating functions of such invariants, which are called the (Ktheoretic) ”big Jfunctions”, play a crucial role in the theory. In this talk, we provide a reconstruction theorem of the permutationinvariant big Jfunction of partial flag varieties (regarded as GIT quotients of vector spaces) using a family of finitedifference operators, based on the quantum Ktheory of their associated abelian quotients which is wellunderstood. Generating functions of Ktheoretic quasimap invariants, e.g. the vertex functions, can be realized in this way as values of various twisted big Jfunctions. We also discuss properties of the level structures as applications of the method. A portion of this talk is based on a joint work with Alexander Givental (my PhD advisor). 

+  Campbell Wheeler  Quantum modularity of quantum invariants: bringing qtilde to qdifference equations  21/06/2022  10:00  1525502  Jussieu  
Recently, there has been increasing interest in solving qdifference equations associated to quantum invariants of 3manifolds as qseries. I will discuss an algorithmic approach to constructing such solutions, studied for example by Dreyfus, and relate such solutions to state integrals of AndersenKashaev. Along with exact computations of monodromy, this proves quantum modularity of such solutions in examples and, in particular, the quantum modularity of the qBorel resummation of the coloured Jones polynomial. This is based on joint work with Garoufalidis, Gu and Mariño. 

+  Eugenii Shustin  Nonnodal real enumerative invariants  16/06/2022  16:00  1516413  Jussieu  
Rational GromovWitten and Welschinger invariants of the plane (or another del Pezo surface) count complex and real rational curves passing through appropriate configuration of points in general position and having nodes as their only singularities. One can count complex curves with nonnodal singularities (cusps etc.) which, under some regularity conditions, always leads to enumerative invariants. In 2006, Welschinger noticed that the count of real plane rational unicuspidal curves does depend on the point constraint, and he suggested a real enumerative invariant counting together the unicuspidal curves, reducible nodal curves, and irreducible curves matching some point and tangency conditions. We address the following question: Does there exist real enumerative invariants counting only rational curves with a given collection of nonnodal singularities and with weights depending only on the topology of the real point set? Theorem 1. In degree 4, such invariants exist only for curves having either one singular point A_5, or one singular point D_4, or one singular point E_6, or three ordinary cusps, provided that, in the latter case, the constraint consists of four pairs of complex conjugate points. All these invariants are positive. Theorem 2. For each degree d>4, there exists an enumerative invariant that counts real rational curves with one singularity of order d1, combined of the transversal local branches of odd orders. Joint work with O. Bojan. 

+  Guillaume Chapuy  bdeformed Hurwitz numbers  14/04/2022  16:00  1516413  Jussieu  
I will talk about the papers arXiv:2109.01499 and arXiv:2004.07824 joint with Maciej Dołęga, and with Valentin Bonzom. By using the deformation of characters of the symmetric group obtained by deforming Schur functions into Jack polynomials, we introduce a oneparameter deformation of Hurwitz numbers, the ``bdeformed Hurwitz numbers''. The GouldenJackson bconjecture from 1996 (and variants) asserts that these numbers are well defined (positive) and have to do with the enumeration of maps on nonoriented surfaces. I will talk about recent progress towards the conjecture, and other developments related to bdeformed "monotone" Hurwitz numbers and \betaensembles of random matrices. 

+  David Holmes  The double ramification cycle for the universal rth root  07/04/2022  16:00  1516413  Jussieu  
The secret goal of this talk is to explain a little of the magic of log line bundles. The vehicle for this will be a story about double ramification cycles for roots of a line bundle. Given a family of curves C/S and a line bundle L on C, the double ramification cycle DR(L) is a class on S measuring the set of points in S over which L is trivial (or more precisely, where L is trivial as a log line bundle). The formal goal of this talk is to describe a lift to the universal rth root of L. More precisely, for a positive integer r we define the stack of rth roots of L, which is a finite flat cover of S of degree r^{2g}. It carries a universal rth root of L (as a log line bundle), and the locus where this rth root is (logarithmically) trivial defines a lift of DR(L) to the stack of rth roots. Pixton's formula for DR(L) admits a fairly straightforward lift to this setting. 

+  Kris Shaw  A tropical approach to the enriched count of bitangents to quartic curves  24/02/2022  15:30  1516413  Jussieu  
Using A1 enumerative geometry Larson and Vogt have provided an enriched count of the 28 bitangents to a quartic curve. In this talk, I will explain how these enriched counts can be computed combinatorially using tropical geometry. I will also introduce an arithmetic analogue of Viro's patchworking for real algebraic curves which, in some cases, retains enough data to recover the enriched counts. This talk is based on joint work with Hannah Markwig and Sam Payne.  
+  Ilia Zharkov  Lagrangian fibrations of the pairofpants  17/02/2022  16:00  1516413  Jussieu  
The pairofpants P is the hypersurface in (C*)^n defined by 1+w_1+...+w_n=0. It is a fundamental building block for many problems in mirror symmetry. I will discuss various Liouville structures on P and a map to the tropical hyperplane which is a Lagrangian torus fibration of P for a particular such structure. I will describe the geometry of the fiber over the origin, which is the Lagrangian skeleton of P.  
+  Séverin Charbonnier  Statistics of multicurves on combinatorial Teichmüller spaces  10/02/2022  16:00  1516413  Jussieu  
I will describe several results regarding the statistics of multicurves on bordered surfaces, whose combinatorial lengths are bounded by a cutoff parameter. After a description of the combinatorial Teichmüller spaces, I will first state how such statistics can be computed by geometric recursion, a recursive procedure akin to topological recursion. Second, the asymptotics of the number of multicurves as the cutoff tends to infinity allow to define a function on combinatorial Teichmüller spaces, that is interpreted as the volume of the combinatorial unit ball of measured foliations; it is the combinatorial analogue of Mirzakhani's B function in the hyperbolic setup. It descends to the moduli spaces and the structure of the latter allows to completely determine its range of integrability with respect to the Kontsevich measure. The range shows surprising dependence on the topology of the surface. Along the talk, I will compare the results with those holding in the hyperbolic world. Joint works with J. E. Andersen, G. Borot, V. Delecroix, A. Giacchetto, D. Lewański and C. Wheeler.  
+  Dhruv Ranganathan  GromovWitten theory via roots and logarithms  03/02/2022  16:00  1516413  Jussieu  
The geometry of logarithmic structures and orbifolds offer two routes to the enumeration of curves with tangencies along a divisor in a projective manifold. The theories are quite different in nature: the logarithmic theory has rich connection to combinatorics and mirror symmetry via tropical geometry, while the orbifold geometry is closer in its formal properties to ordinary GromovWitten theory, and is more computable as a consequence. I will discuss the relationship between the theories, and try to give a sense of where and why they differ. I will then outline the ideas behind recent work with Nabijou and work in progress with Battistella and Nabijou, which determines genus 0 logarithmic GW theory via the orbifold geometry.  
+  Alexander Thomas  Topological field theories from Hecke algebras  28/01/2022  14:00  1516413  Jussieu  
We describe a construction which to a surface and a IwahoriHecke algebra associates an invariant which is a Laurent polynomial. More generally, this construction works for surfaces with boundary and behaves well under gluing, giving a noncommutative topological quantum field theory (TQFT). The invariant polynomial has surprising positivity properties, which are proven using Schur elements. Joint work with Vladimir Fock and Valdo Tatitscheff.  
+  Johannes Nicaise  Variation of stable birational type and bounds for complete intersections  27/01/2022  16:00  1516413  Jussieu  
This talk is based on joint work with John Christian Ottem. I will explain a generalization of results by Shinder and Voisin on variation of stable birational types in degenerating families, and how this can be used to extend nonstable rationality bounds from hypersurfaces to complete intersections in characteristic zero.  
+  Thomas Blomme  Enumération de courbes tropicales dans des surfaces abéliennes  06/01/2022  16:00  1516413  Jussieu  
La géométrie tropicale est un outil puissant qui permet via l'utilisation d'un théorème de correspondance de ramener des problèmes énumératifs algébriques, par exemple compter le nombre de courbes d'un certain degré passant par un nombre de points convenables, à un problème combinatoire. Ces derniers sont plus simples à appréhender mais parfois compliqués à résoudre. De plus, le passage dans le monde tropical permet de définir de mystérieux invariants dits raffinés, obtenus en comptant les solutions d'un problème énumératif avec des multiplicités polynomiales. Dans cet exposé on s'intéressera à l'énumération de courbes et aux invariants raffinés dans les surfaces abéliennes et dans les fibrés en droites au dessus d'une courbe elliptique.  
+  Dimitri Zvonkine  GromovWitten invariants of complete intersections  09/12/2021  16:00  1516413  Jussieu  
We present an algorithm that allows one to compute all GromovWitten (GW) invariants of all complete intersections. The main tool is Jun Li's degeneration formula that expresses GW invariants of one complete intersection via GW invariants of several simpler complete intersections. The main problem is that the degeneration formula does not apply to primitive cohomology classes. To solve this problem we introduce simple nodal GW invariants, show that they can always be computed by degeneration, and then prove that one can recover all GW invariants with primitive cohomology insertions from simple nodal GW invariants. Joint work with H. Arguz, P. Bousseau, and R. Pandharipande.  
+  Sebastian Nill  Extended FJRW theory of the quintic threefold in genus zero  02/12/2021  16:00  1516413  Jussieu  
The LandauGinzburg Amodel of the quintic threefold has a description in terms of higher spin bundles on stable curves. In genus zero the invariants/correlators of the closed rspin theory are given by integration of the top Chern class of the Witten bundle over the moduli space of stable curves. By allowing a new twist equal to 1 at one of the marked points, Alexandr Buryak, Emily Clader and Ran Tessler found a rank one extension of the closed rspin theory in genus zero in 2017. After having a look at this extension, we will see that integration of the fifth power of this top Chern class gives an extension of the FanJarvisRuanWitten (FJRW) theory of the quintic threefold in genus zero. In order to calculate the new invariants, we will mimick the work of Alessandro Chiodo and Yongbin Ruan from 2008 and introduce the Givental formalism. I will sketch how Chiodo's GrothendieckRiemannRoch formula still provides us with a symplectic transformation of the twisted Givental cone. An extension of the Ifunction will arise in the nonequivariant limit of the twisted invariants. This extended Ifunction contains a new term already known as the semiperiod. It is a solution of an inhomogeneous PicardFuchs equation with a constant inhomogeneity. This is work in progress.  
+  Nitin Chidambaram  Shifted Witten classes and topological recursion  25/11/2021  16:00  1516413  Jussieu  
The Witten rspin class is an example of a cohomological field theory which is not semisimple, but it can be "shifted" to make it semi simple. PandharipandePixtonZvonkine studied the shifted Witten class and computed it explicitly in terms of tautological classes using the GiventalTeleman classification theorem. I will show that the Rmatrix of (two specific) shifts can be obtained from two differential equations that are generalizations of the classical Airy differential equation. Using this, I will show that the descendant intersection theory of the shifted Witten classes can be computed using the EynardOrantin topological recursion, and discuss some potential applications. This is based on work in progress with S. Charbonnier, A. Giacchetto and E. GarciaFailde.  
+  Kris Shaw  Real phase structures on matroid fans  15/11/2021  14:00  1525502  Jussieu  
In this talk, I will propose a definition of real phase structures on polyhedral complexes, focusing on matroid fans. I’ll explain that in the case of matroid fans, specifying a real phase structure is cryptomorphic to providing an orientation of the underlying matroid. Then I’ll define the real part of a polyhedral complex with a real phase structure. This determines a closed chain in the real part of a toric variety. This connection to toric geometry provides a homological obstruction to the orientability of a matroid. Moreover, in the case when the polyhedral complex is a nonsingular tropical variety, the real part is a PLmanifold. Moreover, for a nonsingular tropical variety with a real phase structures we can apply the same spectral sequence for tropical hypersurfaces, obtained by Renaudineau and myself, to bound the Betti numbers of the real part by the dimensions of the tropical homology groups. This is partially based on joint work in progress with Johannes Rau and Arthur Renaudineau.  
+  Marvin Hahn  Intersecting PsiClasses on tropical Hassett spaces  07/10/2021  16:00  1516413  Jussieu  
In this talk, we study the tropical intersection theory of Hassett spaces in genus 0. Hassett spaces are alternative compactifications of the moduli space of curves with n marked points induced by a vector of rational numbers. These spaces have a natural combinatorial analogue in tropical geometry, called tropical Hassett spaces, provided by the Bergman fan of a matroid which parametrises certain n marked graphs. We introduce a notion of Psiclasses on these tropical Hassett spaces and determine their intersection behaviour. In particular, we show that for a large family of rational vectors – namely the socalled heavy/light vectors – the intersection products of Psiclasses of the associated tropical Hassett spaces agree with their algebrageometric analogue. This talk is based on a joint work with Shiyue Li.  
+  Andrei Gabrielov  Lipschitz geometry of definable surface germs  02/07/2021  14:00  1516413  Jussieu  
We study outer Lipschitz geometry of surface germs definable in a polynomially bounded ominimal structure (e.g., semialgebraic or subanalytic). By the finiteness theorems of Mostowski, Parusinski and Valette, any definable family has finitely many outer Lipschitz equivalence classes. Our goal is classification of definable surface germs with respect to the outer Lipschitz equivalence. The inner Lipschitz classification of definable surface germs was described by Birbrair. The outer Lipschitz classification is much more complicated. There is also a third, even more complicated, ambient Lipschitz classification problem. Some initial results in this were obtained by Birbrair, Brandenbursky and Gabrielov. Using the contact equivalence classification of Lipschitz functions ("pizza decomposition") by Birbrair et al. and the theory of abnormal surface germs ("snakes") by Gabrielov and Souza, we obtain a decomposition of a surface germ into normally embedded Holder triangles, unique up to outer Lipschitz equivalence. This triangulation, with some additional data ("pizza toppings") is a complete discrete invariant of an outer Lipschitz equivalence class of surface germs. Joint work with L. Birbrair, A. Fernandes, R. Mendes and E. Souza (UFC Fortaleza, Brazil).  
+  Kirsten Wickelgren  An arithmetic count of rational plane curves  06/05/2021  16:00  à distance  
There are finitely many degree d rational plane curves passing through 3d1 points, and over the complex numbers, this number is independent of generally chosen points. For example, there are 12 degree 3 rational curves through 8 points, one conic passing through 5, and one line passing through 2. Over the real numbers, one can obtain a fixed number by weighting real rational curves by their Welschinger invariant, and work of Solomon identifies this invariant with a local degree. It is a feature of A1homotopy theory that analogous real and complex results can indicate the presence of a common generalization, valid over a general field. We develop and compute an A1degree, following Morel, of the evaluation map on Kontsevich moduli space to obtain an arithmetic count of rational plane curves, which is valid for any field k of characteristic not 2 or 3. This shows independence of the count on the choice of generally chosen points with fixed residue fields, strengthening a count of Marc Levine. This is joint work with Jesse Kass, Marc Levine, and Jake Solomon.  
+  Oliver Leigh  Towards a geometric proof of Zvonkine's rELSV formula  25/03/2021  16:00  à distance  
A stable map is said to have "divisible ramification" if the order of every ramification locus is divisible by 𝑟 (a fixed positive integer). In this talk I'll review the theory of stable maps with divisible ramification and discuss how this leads to a geometric framework from which to view and prove Zvonkine's 𝑟ELSV formula. I will also discuss recent results within this framework.  
+  Antoine Toussaint  Comparaison des orientations complexes des courbes réelles planes pseudoholomorphes et algébriques (d'après S. Orevkov)  21/01/2021  16:00  à distance  
L'existence de courbes pseudoholomorphes réelles dans P² dont le schéma complexe n'est pas réalisable par une courbe algébrique du même degré était un problème ouvert jusqu'à ce qu'Orevkov propose une construction de telles courbes en tout degré congru à 9 modulo 12. On présentera la preuve que les schémas induits ne sont pas réalisables par des courbes algébriques, notamment grâce à de nouvelles restrictions sur les orientations complexes d'une courbe algébrique réelle séparante.  
+  Marco Castronovo  Open GromovWitten theory and cluster mutations  14/01/2021  16:00  à distance  
The wallcrossing heuristic in open GromovWitten theory suggests that disk counts with different Lagrangian boundary conditions should be related by simple transformations with a geometric meaning, but examples are scarce above complex dimension two. I will describe examples of Lagrangian tori in complex Grassmannians whose disk counts are related by mutations of a cluster algebra in the sense of FominZelevinsky.  
+  Renata Picciotto  Stable maps with fields to a projective variety  07/01/2021  16:00  à distance  
It is wellknown that genus zero GromovWitten invariants of a subvariety Z⊂X can be recovered, in many cases, from invariants of X by studying obstruction bundles. Unfortunately, this result fails in general for higher genus invariants. The moduli space of stable maps with pfields was first introduced by HuaiLiang Chang and Jun Li, who proved a comparison theorem relating the count of stable maps with pfields to projective space to higher genus GromovWitten invariants of the quintic threefold. The original construction has since seen various generalizations and applications. I will give some background and discuss a very general version of the construction of stable maps with pfields and of the comparison theorem.  
+  Sergej Monavari  DonaldsonThomas type invariants of CalabiYau 4folds  17/12/2020  16:00  à distance  
Classically, DonaldsonThomas invariants are integer valued invariants that virtually count stable coherent sheaves on CalabiYau threefolds. On a CalabiYau fourfold, higher obstructions prevent the existence of virtual fundamental classes in the sense of BehrendFantechi. Nevertheless, BorisovJoyce (via derived differential geometry) and OhThomas (via deformation theory) constructed virtual fundamental classes in this setting, modulo choices of orientations. We review their constructions and explain how to define naturally numerical, Ktheoretic and torusequivariant invariants. Finally we discuss how, conjecturally, DT/PT/GW/GV invariants are related to each other and show instances where the conjectures have been checked. This is based on joint work with Y. Cao and M. Kool.  
+  Alessandro Giacchetto  Geometry of combinatorial moduli spaces and multicurve counts  10/12/2020  16:00  à distance  
The Teichmüller space of bordered surfaces can be described via metric ribbon graphs, leading to a natural symplectic structure introduced by Kontsevich in his proof of Witten's conjecture. I will show that many tools of hyperbolic geometry can be adapted to this combinatorial setting, and in particular the existence of Fenchel–Nielsen coordinates that are Darboux. As applications of this setup, I will present a combinatorial analogue of Mirzakhani's identity, resulting in a completely geometric proof of Witten–Kontsevich recursion, as well as Norbury's recursion for the counting of integral points. I will also describe how to count simple closed geodesics in this setting, and how its asymptotics compute Masur–Veech volumes of the moduli space of quadratic differentials. The talk is based on a joint work with J.E. Andersen, G. Borot, S. Charbonnier, D. Lewański and C. Wheeler.  
+  Omid Amini  Théorie de Hodge pour les variétés tropicales 2  26/11/2020  16:00  à distance  
L'objectif de ces deux exposés est de donner un aperçu de nos travaux sur la théorie de Hodge tropicale. Nous montrons que les groupes de cohomologie des variétés tropicales projectives et lisses vérifient le théorème de Lefschetz difficile et les relations de HodgeRiemann. Nous donnons une description des groupes de Chow des matroïdes en terme de groupes de cohomologie de certaines variétés tropicales projectives et lisses, nos résultats peuvent donc être considérés comme une généralisation du travail d'AdiprasitoHuhKatz à des variétés tropicales plus générales. Nous prouvons également que les variétés tropicales projectives et lisses vérifient l'analogue dans le cadre tropical de la conjecture de monodromiepoids, confirmant une conjecture de Mikhalkin et Zharkov.  
+  Matthieu Piquerez  Théorie de Hodge pour les variétés tropicales 1  19/11/2020  16:00  à distance  
L'objectif de ces deux exposés est de donner un aperçu de nos travaux sur la théorie de Hodge tropicale. Nous montrons que les groupes de cohomologie des variétés tropicales projectives et lisses vérifient le théorème de Lefschetz difficile et les relations de HodgeRiemann. Nous donnons une description des groupes de Chow des matroïdes en terme de groupes de cohomologie de certaines variétés tropicales projectives et lisses, nos résultats peuvent donc être considérés comme une généralisation du travail d'AdiprasitoHuhKatz à des variétés tropicales plus générales. Nous prouvons également que les variétés tropicales projectives et lisses vérifient l'analogue dans le cadre tropical de la conjecture de monodromiepoids, confirmant une conjecture de Mikhalkin et Zharkov.  
+  Tony Yue Yu  Secondary fan, theta functions and moduli of CalabiYau pairs  15/10/2020  16:00  Zoom  
We conjecture that any connected component $Q$ of the moduli space of triples $(X,E=E_1+\dots+E_n,\Theta)$ where $X$ is a smooth projective variety, $E$ is a normal crossing anticanonical divisor with a 0stratum, every $E_i$ is smooth, and $\Theta$ is an ample divisor not containing any 0stratum of $E$, is \emph{unirational}. More precisely: note that $Q$ has a natural embedding into the KollárShepherdBarronAlexeev moduli space of stable pairs, we conjecture that its closure admits a finite cover by a complete toric variety. We construct the associated complete toric fan, generalizing the GelfandKapranovZelevinski secondary fan for reflexive polytopes. Inspired by mirror symmetry, we speculate a synthetic construction of the universal family over this toric variety, as the Proj of a sheaf of graded algebras with a canonical basis, whose structure constants are given by counts of nonarchimedean analytic disks. In the Fano case and under the assumption that the mirror contains a Zariski open torus, we construct the conjectural universal family, generalizing the families of KapranovSturmfelsZelevinski and Alexeev in the toric case. In the case of del Pezzo surfaces with an anticanonical cycle of $(1)$curves, we prove the full conjecture. The reference is arXiv:2008.02299 joint with Hacking and Keel.  
+  Dimitri Zvonkine  Quantum Hall effect and vector bundles over moduli spaces of curves and Jacobians  08/10/2020  16:00  1516413  Jussieu  
Vector bundles of socalled Laughlin states were introduced by physicists to study the fractional quantum Hall effect. Their Chern classes are related to measurable physical quantities. We will explain how they are related to the vector bundle of thetafunctions over the moduli space and to certain vector bundles over the Jacobians. We perform the first steps in the computation of their Chern classes. Work in progress with Semyon Klevtsov.  
+  Elba GarciaFailde  Simple maps, topological recursion and a new ELSV formula  01/10/2020  16:00  1516413  Jussieu  
We call ordinary maps a certain type of graphs embedded on surfaces, in contrast to fully simple maps, which we introduce as maps with nonintersecting disjoint boundaries. It is wellknown that the generating series of ordinary maps satisfy a universal recursive procedure, called topological recursion (TR). We propose a combinatorial interpretation of the important and still mysterious symplectic transformation which exchanges $x$ and $y$ in the initial data of the TR (the spectral curve). We give elegant formulas for the disk and cylinder topologies which recover relations already known in the context of free probability. For genus zero we provide an enumerative geometric interpretation of the socalled higher order free cumulants, which suggests the possibility of a general theory of approximate higher order free cumulants taking into account the higher genus amplitudes. We also give a universal relation between fully simple and ordinary maps through double monotone Hurwitz numbers, which can be proved either using matrix models or bijective combinatorics. As a consequence, we obtain an ELSVlike formula for double strictly monotone Hurwitz numbers.  
+  Johannes Nicaise  Stable rationality of complete intersections (exposé reporté à une date ultérieure)  27/03/2020  10:30  1516413  Jussieu  
After giving an overview of known results about stable rationality of hypersurfaces, I will explain an ongoing project with John Christian Ottem to establish several new classes of stably irrational complete intersections. Our results are based on degeneration techniques and a birational version of the nearby cycles functor that was developed in collaboration with Evgeny Shinder. One technique to construct interesting degenerations is the use of tropical geometry; I will demonstrate this technique by proving the stable irrationality of the quartic fivefold. 

+  Grigory Mikhalkin  Titre à préciser (exposé reporté à une date ultérieure)  26/03/2020  15:30  1516413  Jussieu  
+  Massimo Pippi  Réalisations motivique et ladique de la catégorie des singularités d'un modèle LG twisté (exposé reporté à une date ultérieure)  13/03/2020  10:30  1516413  Jussieu  
Un modèle de LandauGinzburg twisté est un couple (X,s), où X est un schéma (sur une base S) et s est une sectionne globale d'un fibré en droites L sur X. 

+  Karim Adiprasito  From toric varieties to embedding problems and l^2 vanishing conjectures  27/02/2020  16:00  1525502  Jussieu  
I will survey a rather intruiging approach to some problems in geometric topology that start by reformulating them as problems in intersection theory. I will start by explaining, on a specific problem, biased pairing theory, which studies the way that the HodgeRiemann bilinear relation degenerates on an ideal, and review how this limits for instance the complexity of simplicial complex embeddable in a fixed manifold. I will then discuss a conjecture of Singer concerning the vanishing of l^2 cohomology on nonpositively curved manifolds, and use biased pairing theory to relate it to Hodge theory on a Hilbert space that arises as the limit of Chow rings of certain complex varieties. 

+  Conan Leung  Geometry of MaurerCartan equation  06/02/2020  15:30  1525502  Jussieu  
Motivated from Mirror Symmetry near large complex structure limit, a dgBV algebra will be constructed associated to a possibly degenerate CalabiYau variety equipped with local thickening data. Using this, we prove unobstructedness of smoothing of degenerated Log CY satisfying HodgedeRham degeneracy property. 

+  Sybille Rosset  A comparison formula in quantum Ktheory of flag varieties  30/01/2020  16:00  1525502  Jussieu  
I will present here a correspondence between wellchosen quantum Ktheoretical GromovWitten invariants of different flag varieties. I will also discuss how this correspondence implies some finiteness properties of the big quantum Kring of flag varieties. 

+  Sergey Finashin  The first homology of real cubics are generated by real lines  16/01/2020  16:00  1525502  Jussieu  
In a joint work with V. Kharlamov, we suggest a short proof of O. Benoist and O. Wittenberg theorem (arXiv:1907.10859) which states that for each real nonsingular cubic hypersurface X of dimension ≥2 the real lines on X generate the whole group H_1(X(ℝ);ℤ/2). 

+  Sybille Rosset  A comparison formula in quantum Ktheory of flag varieties (reporté)  12/12/2019  16:00  1525502  Jussieu  
I will present here a correspondence between wellchosen quantum Ktheoretical GromovWitten invariants of different flag varieties. I will also discuss how this correspondence implies some finiteness properties of the big quantum Kring of flag varieties. 

+  Danilo Lewanski  ELSVtype formulae  05/12/2019  16:00  1525502  Jussieu  
The celebrated ELSV formula expresses Hurwitz numbers in terms of intersection theory of the moduli space of stable curves. Hurwitz numbers enumerate branched covers of the Riemann sphere with prescribed ramification profiles. Since the original ELSV was found, many more ELSVtype formulae appeared in the literature, especially in connection with EynardOrantin topological recursion theory. They connect different conditions on the ramification profiles of the Hurwitz problem with the integration of different cohomological classes which have been studied independently. We will go through this interplay, focusing on a conjecture proposed by Zvonkine and a conjecture of Goulden, Jackson, and Vakil. In both these conjectures, classes introduced by Chiodo play a key role. 

+  Grigory Mikhalkin  Separating semigroup of real curves and other questions from a 1dimensional version of Hilbert's 16th problem  28/11/2019  15:15  1525502  Jussieu  
Kummer and Shaw have introduced the separating semigroup Sep(S) of a real curve S. The semigroup is made of topological multidegrees of totally real algebraic maps from S to the Riemann sphere and can be considered in the context of a 1dimensional version of Hilbert's 16th problem. We'll explore this point of view and classify Sep(S) for curves of genera up to four. 

+  Yizhen Zhao  LandauGinzburg/CalabiYau correspondence for a complete intersection via matrix factorizations  21/11/2019  16:00  1525502  Jussieu  
In this talk, I will introduce two enumerative theories coming from a variation of GIT stability condition. One of them is the GromovWitten theory of a CalabiYau complete intersection; the other one is a theory of a family of isolated singularities fibered over a projective line, which is developed by Fan, Jarvis, and Ruan recently. I will show these two theories are equivalent after analytic continuation. For CalabiYau complete intersections of two cubics, I will show that this equivalence is directly related  via Chern character  to the equivalences between the derived category of coherent sheaves and that of matrix factorizations of the singularities. This generalizes ChiodoIritaniRuan's theorem matching Orlov's equivalences and quantum LG/CY correspondence for hypersurfaces. 

+  Xavier Blot  The quantum WittenKontsevich series  15/11/2019  10:30  1516413  Jussieu  
The WittenKontsevich series is a generating series of intersection numbers on the moduli space of curves. In 2016, Buryak, Dubrovin, Guéré and Rossi defined an extension of this series using a quantization of the KdV hierarchy based on the geometry of double ramification cycle. This series, the quantum WittenKonstevich series, depends on a quantum parameter. When this quantum parameter vanishes, the quantum WittenKontsevich series restricts to the WittenKontsevich series. In this talk, we will first construct the quantum WittenKontsevich series and then present all the known results about its coefficients. Surprisingly, a part of these coefficients are expressed in terms of Hurwitz numbers. 

+  Hülya Argüz  Real Lagrangians in CalabiYau Threefolds  18/10/2019  10:30  1516413  Campus Pierre et Marie Curie  
We compute the mod 2 cohomology of the real Lagrangians in CalabiYau threefolds, using a long exact sequence linking it to the cohomology of the CalabiYau. We will describe this sequence explicitly, and as an application will illustrate this computation for the quintic threefold. This is joint work with Thomas Prince and with Bernd Siebert. 

+  Yanqiao Ding  Genus decreasing phenomenon of higher genus Welschinger invariants  27/09/2019  10:30  Jussieu, salle 1516413  
Shustin introduced an invariant of del Pezzo surfaces to count real curves of positive genera. By considering the properties of these invariants under Morse transformation, we found a genus decreasing phenomenon for these invariants. In this talk, we will present a genus decreasing formula for these invariants and discuss possible generalization of it. 

+  Eugenii Shustin  Singular Welschinger invariants  28/06/2019  10:00  Jussieu, salle 1516413  
We discuss real enumerative invariants counting real deformations of plane curve singularities. A versal deformation base of a plane curve singularity contains local Severi varieties that parameterize deformations with a given deltainvariant. The local Severi varieties are analytic space germs and their (complex) multiplicities were computed by Beauville, FantecciGoettschevan Straten, and Shende. For the equigeneric locus (local Severi variety corresponding to the maximal deltainvariant), a real multiplicity was introduced by ItenbergKharlamovSh. as a Welschingertype signed count of certain equigeneric deformations. We show that similar real multiplicities can be defined for some other local Severi varieties as well as for all equiclassical loci (which count equigeneric deformations with a given number of cusps). We exhibit some examples and state open problems.  
+  Albrecht Klemm  Topological String on compact CalabiYau threefolds  21/06/2019  10:30  Jussieu, salle 1516413  
We review the worldsheet derivation of the holomorphic anomaly equations fulfilled by the all genus topological string partition function $Z$ on CalabiYau 3folds $M$. Interpreting $Z$ as a wave function on $H_3(M, R)$ these equations can be viewed as describing infinitesimal changes of the symplectic frame. A recursive solution for $Z$ to high genus is provided using modular building blocks obtained by the periods of $M$ as well as constraints on the local expansion of $Z$ near singular loci in the complex moduli space of M in appropriate symplectic frames. Some recent applications of these ideas to elliptic fibred CalabiYau spaces are given.  
+  Alex Degtyarev  Tritangents to sextic curves via Niemeier lattices  14/06/2019  10:30  Jussieu, salle 1525502  
I suggest a new approach, based on the embedding of the (modified) NéronSeveri lattice to a Niemeier lattice, to the following conjecture: The number of tritangents to a smooth sextic is 72, 66 (each realized by a single curve), or less. The maximal number of real tritangents to a real smooth sextic is 66. (Observed are all counts except 65 and 63.) The computation becomes much easier (linear algebra in wellstudied lattices rather than abstract number theory), and it has been completed for all but Leech lattices. At present, I am 99% sure that I can eliminate the Leech lattice, settling the above conjecture.  
+  Alexander Alexandrov  Constellations, Weighted Hurwitz numbers, and topological recursion (a mathematical physicist's view)  19/04/2019  10:30  Jussieu, salle 1516413  
In my talk I will discuss some elements of the proof of the topological recursion for the weighted Hurwitz numbers. The main ingredient is the taufunction  the all genera generating function, which is a solution of the integrable KP or Toda hierarchy. My talk is based on a series of joint papers with G. Chapuy, B. Eynard, and J. Harnad.  
+  Florent Schaffhauser  Topologie des variétés de représentations de groupes fuchsiens  29/03/2019  10:30  Jussieu, salle 1516413  
Le but de l'exposé est de présenter quelques progrès récents dans l'étude la topologie des variétés de représentations de groupes fuchsiens. On s'intéressera principalement à deux exemples, les fibrés vectoriels sur les courbes algébriques réelles et les composantes de Hitchin pour les groupes fondamentaux orbifold, et on montrera par exemple que la composante de Hitchin d'une surface orientable à bord (introduite par McShane et Labourie en 2009) est homéomorphe à un espace vectoriel dont la dimension est donnée par la même formule que celle obtenue par Hitchin dans le cas des surfaces fermées. Plus généralement, nous verrons que les composantes de Hitchin orbifold fournissent des sousvariétés totalement géodésiques contractiles des composantes de Hitchin classiques (pour toute métrique invariante sous l'action du groupe modulaire), dont on peut calculer la dimension et montrer qu'elles fournissent des exemples d'espaces de Teichmüller supérieurs, au même titre que les composantes de Hitchin associées aux groupes de surfaces.  
+  Xujia Chen  Kontsevichtype recursions for counts of real curves  15/03/2019  10:30  Jussieu, salle 1516413  
+  Adrien Sauvaget  MasurVeech volumes and intersection theory on the projectivized Hodge bundle  08/03/2019  10:30  Jussieu, salle 1516413  
In the 80's Masur and Veech defined the volume of moduli spaces Riemann surfaces endowed with a flat metric with conical singularities. We show that these volumes can be expressed as intersection numbers on the projectivized Hodge bundle over the moduli space of curves (this is a joint work with D. Chen, M. Moeller, and D. Zagier).  
+  Paolo Rossi  Quadratic double ramification integrals and KdV on the noncommutative torus  22/02/2019  10:30  Jussieu, salle 1516413  
It's a result of Richard Hain that the restriction of the double ramification cycle to the space of compact type curves (i.e. stable curves with no nonseparating nodes) is Θg/g!, where Θ is the theta divisor in the universal Jacobian (suitably pulled back to the moduli space itself via the marked points). A natural completion of this class is given by exp(Θ), which gives an infinite rank partial cohomological field theory. To such an object one can attach a double ramification hierarchy (thereby putting into play a second DR cycle, hence the "quadratic" in the title). It is possible to compute this hierarchy and trade its infinite rank for an extra space dimension, hence obtaining an integrable hierarchy in 2+1 dimensions which is the natural extension of the usual KdV hierarchy on a noncommutative torus. Its quantization is also provided, obtaining an integrable (2+1) nonrelativistic quantum field theory on the noncommutative torus.  
+  Pierrick Bousseau  Sur les nombres de Betti des espaces de modules de faisceaux semistables sur le plan projectif  08/02/2019  10:30  Jussieu, salle 1516413  
Je vais présenter un nouvel algorithme, à l’allure tropicale, calculant les nombres de Betti (pour la cohomologie d’intersection) des espaces de modules de faisceaux semistables sur le plan projectif. Je finirai par une application à une question a priori sans rapport en théorie de GromovWitten.  
+  Thomas Blomme  Scattering diagrammes, indices quantiques et géométrie énumérative réelle  01/02/2019  10:30  Jussieu, salle 1516413  
En géométrie énumérative, l'approche tropicale est parfois fort utile pour calculer effectivement certains invariants de part la nature combinatoire de cette dernière. De plus, sa richesse structurelle permet en fait de calculer bien plus que les invariants qui nous intéressent, et c'est par exemple le cas des polynômes de BlockGöttsche. Dès lors se pose la question de l'interprétation de tels invariants en géométrie classique et de nombreuses restent encore ouvertes. Dans le cas des courbes planes, Mikhalkin propose d'interpréter le polynôme de BlockGöttsche comme un comptage de courbes réelles satisfaisant des conditions de tangence à l'infini en les discriminant suivant la valeur que prend l'aire de leur amibe. Nous allons tenter de poser les bases de ce que pourrait être un analogue en dimension supérieure.  
+  Sergey Finashin  Welschinger weights and Segre indices for real lines on real hypersurfaces  25/01/2019  10:30  Jussieu, salle 1516413  
In a joint work with V.Kharlamov, we explained how one may count real lines on real hypersurfaces (when their number is generically finite) with signs, so that the sum is independent of the choice of a hypersurfaces. These signs were assumed conjecturally to be equal to some multidimensional version of Welschinger weights. After elaborating this version of the weights, we proved this conjecture. We developed also a more geometric way of calculation: using the idea of Segre, who introduced two species of real lines on a cubic surface: hyperbolic and elliptic.  
+  Oliver Lorscheid  Tropical scheme theory  18/01/2019  10:30  Jussieu, salle 1516413  
In 2013, Giansiracusa and Giansiracusa have found a way to use F1geometry for tropical geometry. More precisely, they define the schemetheoretic tropicalization of a classical variety and show that the settheoretic tropicalization can be retrieved as the set of Trational points.
The schemetheoretic tropicalization carries more information than the settheoretic tropicalization. For example, it knows about the Hilbert polynomial of the classical variety and the weights of the (maximal cells of the) settheoretic tropicalization. There are hopes that this will be useful for future developments, such as tropical sheaf cohomology, a cohomological approach to intersection theory, flat tropical families, and more. However, some fundamental problems remain unsolved so far. For example, it is not clear how to approach dimension theory or decompositions into irreducible components. It is not even clear what a good notion of a tropical scheme should be since the class of semiring schemes contains too many and pathological objects. In this talk we give an introduction to tropical scheme theory and an overview of this circle of ideas. 

+  Guillaume Chapuy  Constellations, Weighted Hurwitz numbers, and topological recursion (a combinatorialist's view)  14/12/2018  10:30  Jussieu, salle 1516413  
+  Dimitri Zvonkine  An introduction to the double ramification hierarchies by Buryak and Rossi  07/12/2018  10:30  Jussieu, salle 1516413  
+  Hülya Argüz  Tropical and log corals on the Tate curve  16/11/2018  10:30  Jussieu, salle 1516413  
We will discuss an algebrogeometric approach to the symplectic cohomology ring, in terms of tropical geometry and punctured log GromovWitten theory of AbramovichChenGrossSiebert. During this talk, we will restrict ourselves to the Tate curve, the total space of a degeneration of elliptic curves to a nodal elliptic curve. To understand the symplectic cohomology of the Tate curve (minus its central fiber), we will go through the Fukaya category of the elliptic curve and describe this category using tropical Morse trees introduced by AbouzaidGrossSiebert.  
+  Marco Robalo  Matrix Factorizations and Vanishing Cycles  19/10/2018  10:30  Jussieu, salle 1516413  
In this talk I will describe a joint work with B. Toen, G. Vezzosi and A. Blanc, relating categories of matrix factorisations to sheaves of vanishing cycles. Most of the talk will be a review of the theory of vanishing cycles and matrix factorisations and how they can be related in the theory of motives.  
+  Nicolas Perrin  Positivité pour la Kthéorie quantique de la grassmannienne  12/10/2018  10:30  Jussieu, salle 1516413  