Videos

How to be exceptional

Presenter
November 13, 2025
Abstract
Exceptional types/cases tend to be avoided as they often exhibit sporadic or deviant behavior compared to the families in a classification scheme, such as finite/affine Cartan types or complex reflection groups. Computations done with infinite series also tend to be avoided because of issues with precision. The goal of this talk is to show that exceptional cases are not scary by demonstrating how we can use computational tools to better understand their mysteries. We will primarily focus on the representation theory of algebraic objects in Cartan type E (both finite and affine) to showcase how techniques can work in general and that understanding exceptional cases can often be beneficial in giving uniform proofs. Part of this talk is based on joint work with Se-jin Oh.