Speaker:  Peng Shan (Tsinghua)

Title:  Modularity for W-algebras, affine Springer fibres and associated variety

Abstract: I will explain a bijection between admissible representations of affine Kac-Moody algebras and fixed points in affine Springer fibres. I will also explain how to match the modular group action on the characters of representations with the one defined by Cherednik in terms of double affine Hecke algebras, and extensions of these relations to representations of W-algebras. If time permits, I will discuss some extension of these results to non-admissible levels and some conjectures about their associated varieties.

This is based on joint work with Dan Xie, Wenbin Yan and Qixian Zhao.