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

Résumé: On connaît un bon nombre d'incarnations classiques de la cohomologie des groupes de Lie simples, de nature algébrique, analytique ou géométrique. Nous proposons de l'aborder avec un outil plus familier en systèmes dynamiques: le bord de Furstenberg et sa

Abstract: I will give a geometric construction of an automorphism of a rational surface that has no periodic curves.  The construction is elementary, exploiting the geometry of the Bertini involution on a degree 1 del Pezzo surface.  The rational surface

Résumé : J'expliquerai comment transformer l'ensemble des polygones de Newtonengendrés par un processus de résolution toroïdale d'une singularité de courbeplane en un lotus. Il s'agit d'un complexe simplicial bidimensionnel particulier,qui unifie les invariants combinatoires classiques associés à la singularité. C'est