Categorical symmetries in representation theory (2018-2021)
Abstract
The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. Progress on this project would be a major advance in pure mathematics with potentially dramatic consequences in all the related fields.
