Algebraic Lie Theory and Symplectic Geometry

The workshop will focus on the relationship between representation theory and the following topics:

-Sheaves and algebras arising from deformation quantization of symplectic resolutions
-Quantum cohomology of quiver varieties
-Symplectic duality and Koszul duality
-Relation with categorifications of Kac-Moody algebras and of braid groups
-Relation with knot theory
-Relation with cluster algebras.

This is the first workshop of a series of workshops on

Geometric Representation Theory and Related Topics

which will be held biennially at Tsinghua Sanya International Mathematics Forum. Each workshop will focus on a specific theme related to geometric representation theory.

Representation theory is the study of the basic symmetries of mathematics and physics. The primary aim of the subject is to understand concrete linear models for abstract symmetry groups. A signature triumph of the past century is our understanding of the representation theory and harmonic analysis of compact Lie groups. Geometric representation theory seeks to understand these groups and their representations as a consequence of more subtle but fundamental structures. Among these spaces and resulting representation theories are the flag manifolds (Beilinson-Bernstein localization), Deligne-Lusztig varieties (representations of finite groups of Lie type), Springer fibers (representations of Weyl groups and Hecke algebras), quiver varieties (representations of quantum groups), affine Grassmannians (geometric Satake correspondence) and general moduli spaces of bundles on curves, buildings, Drinfeld modular varieties and Shimura varieties (realizing representations of p-adic or adelic points of reductive groups). Modern geometric representation theory borrows methods from algebraic geometry (including derived algebraic geometry), sheaf theory (especially perverse sheaves) and higher category theory (sometimes in the form of topological field theories) to study the spaces mentioned above, construct representations of various groups and algebras and prove properties about them.

The main aim of this series of workshops is to bring experts and researchers worldwide together to communicate new developments and new directions on geometric representation theory and related topics, as well as to provide opportunities for young scholars and students from China to learn the relevant subjects.

Organizers

NameUniversity
Bangming DengTsinghua University
Peng ShanCNRS-Université Paris-Sud
Zhiwei YunStanford University
Xinwen ZhuCalifornia Institute of Technology