| Equipe(s) | Responsable(s) | Salle | Adresse |
|---|---|---|---|
| J.-Y. Charbonnel, E. Letellier, R. Rentschler, S. Riche, M. Varagnolo |
175 rue du Chevaleret - 75013 Paris |
| Orateur(s) | Titre | Date | Début | Salle | Adresse | ||
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| + | Hanno Becker | Models for Singularity Categories and Applications to Khovanov-Rozansky Homology. | 05/06/2015 | 11:00 | Sophie Germain en salle 2018 | ||
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| + | Hiraku Nakajima | Towards a mathematical definition of Coulomb branches of 3-dimensional N=4 gauge theories. | 13/03/2015 | 14:00 | Sophie Germain en salle 0014 | ||
| Consider the 3-dimensional N=4 supersymmetric gauge theory associated with a compact Lie group G and its quaternionic representation M. Physicists study its Coulomb branch, which is a noncompact hyper-Kähler manifold, such as instanton moduli spaces on $R^4$, SU(2)-monopole moduli spaces on $R^3$, etc.
In this talk, we propose a mathematical definition of the coordinate ring of the Coulomb branch, using the vanishing cycle cohomology group of a certain moduli space for a gauged $\sigma$-model on the 2-sphere associated with (G,M). |
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| + | Ruslan Maksimau | Algèbres KLR et actions catégoriques. | 27/02/2015 | 11:00 | Sophie Germain en salle 2018 | ||
| L'algèbre de Lie affine \hat sl_n est incluse dans l'algèbre de Lie affine \hat sl_n+1. Soit C une catégorie abélienne qui admet une action de \hat sl_n+1. Je vais expliquer pourquoi dans cette situation on obtient automatiquement une \hat sl_n-action sur une sous-catégorie de C. Le point clé de la preuve est que l'algèbre KLR d’un n-cycle est isomorphe à un sous-quotient de l'algèbre KLR d’un (n+1)-cycle. |
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| + | Azat Gainutdinov | From affine Temperley-Lieb algebras at roots of unity to highest-weight categories of Virasoro algebra modules. | 06/02/2015 | 11:00 | Sophie Germain en salle 2018 | ||
| Temperley-Lieb algebras of finite/affine type are rank-one quotients of the finite/affine Hecke algebras and known in the theory of invariants as Schur-Weyl duals to the Lusztig's specialization of the (affine) quantum algebra for sl(2). In the talk, I will present an explicit inductive system construction for finite TL algebras at a root of unity that gives the Virasoro in the limit. On the abstract grounds, I will also discuss my recent result on a connection between representation theory of affine (and finite) TL algebras at all roots of unity cases and the Virasoro algebra at critical values of central charge. |
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| + | Conférence Théorie des Représentations | 12/01/2015 | 09:00 | Amphi Turing (12,13,14) et Amphi Gouges (15,16) | |||
| http://yu.perso.math.cnrs.fr/ANR/Paris2015.html |
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| + | Colloque Tournant à Orsay | 07/01/2015 | 14:00 | ||||
| https://sites.google.com/site/olivierschiffmann/home/colloque-tournant-2015 |
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| + | François Costantino | Sur les TQFTs non semi-simples obtenues des représentations de U_q(sl_2) aux racines de l'unité. | 05/12/2014 | 11:00 | Sophie Germain en salle 2035 | ||
| Récemment, en plusieurs collaborations avec Bertrand Patureau-Mirand, Nathan Geer et Christian Blanchet, nous avons construit une nouvelle famille de ``théories topologiques des champs quantiques`` (TQFT) dont un des ingredients essentiels est l'utilisation d'une catégorie non semi-simple de représentations d'une version du groupe quantique $U_q(sl_2)$ aux racines de l'unité. Le but de cet exposé est de donner une introduction à ces constructions pour des non-topologues. Je commencerai par rappeler la définition de TQFT et discuter comment en construire.
Après avoir fait un survol sur le lien entre TQFTs et théories des représentations des groupes quantiques, j'introduirai la version ``déroulée'' de $U_q(sl_2)$ ; puis, je discuterai la structure de la catégorie de ses représentations. Si le temps me le permettra, je terminerai en essayant de mettre en evidence les enjeux et les difficultés de notre construction, ainsi que les pistes de recherche ouvertes. |
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| + | Ivan Cherednik | The PBW-filtration and nonsymmetric Macdonald polynomials. | 28/11/2014 | 11:00 | Sophie Germain en salle 2012 | ||
| A fundamental but difficult question in the representation theory is counting the PBW-degree, the minimal length of the products of f-operators for all positive roots (not only simple) needed to reach any vector from the highest vector.
E. Feigin, G. Fourier and P. Littlemann constructed the corresponding abstract PBW-basis for the Lie algebras of types A,C. A surprising recent conjecture due to the speaker, D. Orr and E. Feigin connects the PBW-degrees in Demazure level-one (affine) modules with the nonsymmetric Macdonald polynomials at t=infinity. This somewhat resembles the link of the BK-filtrartion to the Hall-Littlewood polynomials (q=0); both filtrations are related to the Kostant q-partition functions, though in very different ways. The conjecture was justified by the speaker and E. Feigin for extremal vectors in finite-dimensional irreducible representations (the ``top'' part of the corresponding Demazure module) for classical Lie algebras and G2. |
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| + | Evgeny Gorsky | Torus knots and Cherednik algebras. | 21/11/2014 | 11:00 | Sophie Germain en salle 2012 | ||
| I will describe a relation between the characters of certain representations of rational Cherednik algebras and HOMFLY invariants of torus knots. Conjecturally, these representations can be equipped with an extra filtration such that the associated graded spaces match the Khovanov-Rozansky homology and the homology of certain explicit sheaves on the Hilbert scheme of points. |
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| + | Jyun-Ao Lin | L'algèbre de Hall sphérique sur une courbe projective lisse pondérée. | 14/11/2014 | 11:00 | Sophie Germain en salle 2012 | ||
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| + | Iván Angiono | Nichols algebras of diagonal type and Lie (super)algebras. | 07/11/2014 | 11:00 | Sophie Germain en salle 2012 | ||
| The study of finite-dimensional Nichols algebras of diagonal type is a fundamental step towards the classification of finite-dimensional pointed Hopf algebras. But these algebras are interesting by themselves. This family of Nichols algebrasinclude the positive parts of the quantized enveloping superalgebras of finite-dimensional simple Lie superalgebras over a field of characteristic 0.
The classification of Nichols algebras of diagonal type is possible thanks to the introduction of a powerful tool, the Weyl groupoid. This groupoid relates the different Nichols algebras with the same Drinfeld double. Contragredient Lie superalgebras have an analogous phenomenon; there exist different matrices (and parities of the generators) such that the attached Lie superalgebras are isomorphic. In this talk we recall the definition of these three objects: Nichols algebras, Weyl groupoid and contragredient Lie superalgebras (over a field of arbitrary characteristic). We will explain a close relation between some exceptional examples in positive characteristic, i.e. with no analogues in characteristic zero, and Nichols algebras of unidentified type, that is, neither coming from quantized enveloping superalgebras over a field of characteristic zero nor of standard type. |
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| + | Gwyn Bellamy | Counting resolutions of symplectic quotient singularities. | 24/10/2014 | 11:00 | Sophie Germain en salle 2012 | ||
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| + | Tomoyuki Arakawa | Nilpotent orbits, affine Kac-Moody algebras, and affine W-algebras. | 17/10/2014 | 11:00 | Sophie Germain en salle 2012 | ||
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