Abstract 

The topic of this conference is geometric representation theory, automorphic forms and their connections. In recent years, there have been spectacular progresses in the study of geometric constructions of Lie-theoretic objects, including new families of quantum groups, and in the realization of their representations using new types of geometric invariants such as critical cohomology. At the same time, the branches of number theory that are most directly related to the arithmetic of automorphic forms have seen much progress, with the resolution of many longstanding conjectures. These breakthroughs have also largely been achieved by the discovery of new geometric techniques and insights. The conference will focus on the recent results in both areas, as well as on the connections between them. 

Description of the aim 

Geometric representation theory studies representations (of various symmetry objects like algebraic groups, Hecke algebras, quantum groups, quivers etc.) by realizing them through geometric means, e.g., by geometrically defined actions on sections of various bundles or sheaves, as in geometric quantization (see at orbit method), D-modules, perverse sheaves, deformation quantization modules… Deep connections between representation theory and automorphic forms have been established, using a wide range of methods from algebra, geometry and analysis.  

The goal of the conference is to bring leading experts in representation theory and automorphic forms to discuss the most recent progress in the field, fostering connections between different subjects. The hope is that a broad discussion of recent ideas and techniques would lead to new breakthroughs in the field.