Modularity for W-algebras, Affine Springer Fibres and Associated Variety

Explore a mathematical lecture from the Arithmetic Quantum Field Theory Conference where Peng Shan from Tsinghua University delves into the intricate relationships between admissible representations of affine Kac-Moody algebras and fixed points in affine Springer fibres. Learn about the matching of modular group actions on representation characters with those defined by Cherednik using double affine Hecke algebras, and discover how these relationships extend to W-algebra representations. Gain insights into potential extensions of these results to non-admissible levels and examine conjectures about their associated varieties, drawing from collaborative research with Dan Xie, Wenbin Yan, and Qixian Zhao.