Justin Wu L&S Math & Physical Sciences
Duality for elliptic character sheaves
In the latter half of the 20th century, two seemingly unrelated innovations occurred. The first was Drinfeld’s realization that certain important functions in number theory could be understood as functions on a geometric object: the space of G-bundles. The second was Lusztig’s approach to studying representations of finite groups using character sheaves. The bridge between these two topics is an observation by Looijenga (unpublished) that leads to a generalization of character sheaves to loop groups using the space of G-bundles.
The goal of this project is to understand dualities in this theory of “elliptic character sheaves”. More precisely, the hope is to establish a relationship between the building blocks of elliptic character sheaves for a group G and its dual group G^. Progress in this direction will clarify the role of elliptic character sheaves in the Betti geometric Langlands program, developed by Ben-Zvi & Nadler.
Message To Sponsor
Thank you Tu & Wang for sponsoring my SURF project! I found my research experience very exciting, and has led to me learning many new things in math. As a result, I feel more confident in my abilities to do research, and my interest in mathematics has grown further.