Abstract 

We will explain a bijection between admissible representations of affine Kac-Moody algebras and fixed points in affine Springer fibers. Furthermore, we can also match the modular group action on the characters with the one defined by Cherednik in terms of double affine Hecke algebras. We will also explain how to extend these relations to representations of W-algebras. This is based on joint work with Peng Shan and Dan Xie.

About the speaker 

I spent my undergraduate at Tsinghua University from 2003 to 2007. Then I pursued the Ph.D. at YITP, Stony Brook University under the advice of professor Leonardo Rastelli. After graduating from Stony Brook in 2012, I spent three years at Caltech Theory Group as a postdoctoral researcher (Sherman-Fairchild fellow). After that I was a postdoctoral researcher at CMSA, Harvard University from 2015 to 2017. In 2017, I joined Yau Mathematical Sciences Center, Tsinghua University as a faculty member.

My research focuses on various aspects of supersymmetric theories and superconformal theories (SCFT) with various supersymmetry (SUSY) in various dimensions. Moduli spaces of vacuum, exact observables, dynamics (perturbative and non-perturbative), and etc play an important role in the contemporary of modern physics and mathematics.