# Geometry and Representation Theory

Geometric methods have been one of the major trends in the modern development of representation theory. Perhaps the most important turning point is the appearance of the Kazhdan-Lusztig conjecture on the characters of irreducible highest weight representations of semisimple Lie algebras that was proved by Beilinson-Bernstein and Brylinski-Kashiwara by the method of D-modules and the Riemann-Hilbert correspondence. The development in this field has been accelerated by the influence of quantum field theory and of string theory, which in particular led Beilinson and Drinfeld to introduce the influential geometric Langlands program.

At the same time, the importance of studying infinite dimensional algebras such as affine Kac-Moody algebras or, more generally, as vertex algebras (e.g. (affine) W-algebras) became apparent.

For instance, vertex algebras or chiral algebras, their geometric versions, have been playing an essential role in the geometric Langlands program. Affine Kac-Moody algebras also play a fundamental role in the theory of categorification, which was developed by Rouquier, Ariki, Brundan-Kleshchev, Stroppel and many others. Furthermore, the appearance of the AGT conjecture in physics led many researchers towards the so-called W-algebras introduced and developed by Zamolodchikov, Fateev-Lukyanov, Feigin-Frenkel and Kac-Roan-Wakimoto, while their finite-dimensional analogues, the finite W-algebras introduced by Premet, have caught attention for different reasons that are mostly related with more classical problems of representation theory.

The aim of this conference is to bring together researchers in representation theory coming from different backgrounds, and to present the above described recent developments in representation theory that interacts with other areas of Mathematics, such as mathematical physics or algebraic geometry, exploiting various branches of Lie Theory. In particular, we want to emphasize the use of geometric methods in representation theory.

The main areas that we wish to deal with in this workshop are the following:

- Algebraic D-modules/Intersection cohomology, Vertex algebras, Affine Grassmanians and their variants, Spherical varieties.

**The first week, January 16 - 20, 2017, will be devoted to mini-course and talks given by participants. **Schedule (pdf)

**The second week, January 23 - 27, 2017, will be devoted to talks given by participants. **Schedule (pdf)