Abstract: Ever since the classical theory of a highest-weight classification, one ever-present strength of Lie theory, was its ability to produce effective and elegant descriptions of collections of simple objects in categories of interest. A cornerstone feat achieved by Zelevinsky

Résumé : Dans cet exposé, j'introduirai la notion d'ensemble basique unitriangulaire et essayerai de motiver leur utilité en théorie des représentations modulaires des groupes finis. Je présenterai également quelques résultats récents obtenus sur le sujet en collaboration avec Gramain-Jacon, et avec

Résumé : Dans cet exposé je parlerai des matrices de décomposition pour les groupes réductifs finis tels que GL(n,q), Sp(2n,q), SO(n,q)... J'expliquerai quels sont les caractères à considérer pour obtenir un ensemble basique et pourquoi ils permettent de mettre la

Abstract: The SYZ conjecture is a conjectural geometric explanation of mirror symmetry. Based on this, Kontsevich and Soibelman proposed a non-archimedean approach to mirror symmetry. This led to the notion of essential skeleton and the construction of non-archimedean SYZ fibrations

Abstract: The Cox ring of an algebraic variety (satisfying some natural conditions) is a very rich invariant.  It was introduced by Cox in 1995 for the study of toric varieties, and then generalized to normal varieties by  Arzhantsev, Berchtold and Hausen.

Abstract : Hall algebras and related notions play a prominent role in the modern representation theory. In their present form, they first appeared in a series of papers by Ringel on quantum groups. After giving all the necessary definitions, I will explain the interplay

Exposés dans le cadre de la deuxième année de thèse. Chaque exposé durera 30 minutes et sera en anglais. First Talk :  « Brauer algebras of complex reflection groups » by Ilias Andreou (LMV) Abstract :  Brauer algebras were introduced by Brauer in 1937

Abstract: Let G be a quasi-split form of a symplectic, unitary or orthogonal group defined over a non-archimedean local field of odd residue characteristic. Every smooth irreducible representation of a p-adic classical group G contains a semisimple character, a certain arithmetic

Abstract :  We describe a construction which to a surface and a Iwahori-Hecke 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 non-commutative topological