D-modules and representation theory -- SMRI Seminar Series

D-modules and representation theory 

Lecturers: Dragan Milicic, Geordie Williamson + others 

Fridays 2.30pm - 5pm 
Quad S223 starting Week 2 (August 11).  

Abstract: D-modules provide an algebraic language for studying systems of linear partial
differential equations.  In some sense the idea goes back to Riemann: rather than
studying some complicated function directly, study the equations which it satisfies and
try relate these equations on different spaces.  D-module have found major applications
in representation theory, algebraic analysis, algebraic geometry and mathematical
physics.  his course will introduce the basics of the theory of algebraic D-modules
(following some famous notes of Bernstein).  The localization theorem of Beilinson and
Bernstein will be discussed in detail.  We will then move on to other applications in
representation theory.  Namely we hope to explain how certain old results of
Harish-Chandra and Langlands become quite transparent in the language of D-modules.  

We will also have a short workshop in the semester break featuring lectures by Kari
Vilonen and Dougal Davis, who have recently used D-modules and mixed Hodge modules to
make progress on fundamental problems in the representation theory of real Lie groups.

https://sites.google.com/view/2023dmodules/home