An informal introduction to categorical representation theory
This is the website for a mini-course held on Zoom in Spring 2022 as part of the Yale Algebra and Geometry lecture series.
Links
For logistical details, including how to attend, see the website for the Yale Algebra and Geometry lecture series here.
A brief description of the course may be found here, and the survey we will be following may be found here.
Lectures
February 3rd - Overview of the course. Preliminaries on finite groups and their Hecke algebras. Notes and recording.
February 10th - Preliminaries on finite groups and their Hecke algebras, continued. Notes and recording.
February 17th - Hecke algebras for principal series. Notes and recording.
February 24th - Categorification, function - sheaf dictionary. Notes and recording.
March 3rd - Function - sheaf dictionary, continued. Notes and recording.
March 10th - Function-sheaf dictionary, finished, the categorical group algebra. Notes and recording.
March 17th - Artin comparison, introduction to D-modules. Notes and recording.
March 31th - Introduction to D-modules, continued, Riemann--Hilbert correspondence. Notes and recording.
April 7th - Categorical representations of groups, I. Notes and recording.
April 14th - From triangulated to dg-categories, I. Notes and recording.
April 21st - From triangulated to dg-categories, II. Notes and recording.
April 28th - Categorical representations of groups, II. Notes and recording.
May 5th - Categorical representations of groups III - localization. Notes and recording.