Modular Representation Theory

Course Schedule

This course is designed to show some of the beautiful mathematics in modern modular representation theory. The first 5 or 6 lectures are introductory, and those that follow will be on specific topics in the theory.

This course is running during the first half of 2023, at the University of Sydney. The seminars take place  on Thursdays at 4 –6pm in Carslaw 535 (see a map). There is no need to sign up, everyone is welcome! 

Each lecture will be recorded and added to the YouTube playlist on the SMRI YouTube channel.

Useful Resources:

This website of Tim Dokchitser is a fantastic resource for characteristic zero representation theory of finite groups, it has an enormous number of examples with detailed information.

Notes:

Lecture 1: Representations and Characters.

Lecture 2: Clifford Theory and some modular basics.

Lecture 3: CDE triangle and modular characters.

Lecture 4:

Lecture 5: Green's Correspondence.

Lecture 6: Stable equivalence of modules.

Lecture 7: Going into the example SL_2(F_p).

Lecture 8: Brauer trees and Broue's abelian defect conjecture.

Lecture 9: The Vershik-Okounkov approach to symmetric group representations.

Lecture 10: The Vershik-Okounkov approach, continued.

Lecture 11: Broue's conjecture for symmetric groups.

Lecture 12: sl2 categorification.

Lecture 13: Modular Deligne-Lusztig theory.

YouTube playlist: