colloquium

Minimal length elements: some interaction between

Speaker: Xuhua He (University of Maryland)

Title: Minimal length elements: some interaction between combinatorics, representation theory, and arithmetic geometry

Abstract: The study of minimal length elements in a conjugacy class of a Weyl group arises in the study of representation theory. Minimal length elements have many remarkable combinatorial properties.
The proof, however, is inspired by arithmetic geometry. In the first half of this talk, I will discuss these combinatorial properties, and some stories which lead to the discovery of the proof.

In the second half of this talk, I will talk about some applications of these combinatorial properties to representation theory and arithmetic geometry. I will explain how some ideas in arithmetic
geometry lead to new discoveries in representation theory, and vice versa.

Bio: Prof Xuhua He received his PhD in mathematics from Massachusetts Institute of Technology in 2005. He worked for the Institute for Advanced Study and Stony Brook University from 2005-2008. After that,
he moved to Hong Kong and stayed there for six years. He is currently a Professor of Mathematics at University of Maryland.

Prof He's research interests lie at the crossroads of algebraic group theory, representation theory, combinatorics, algebraic geometry, and arithmetic geometry. He received the Morningside Gold Medal at the 6th
International Congress of Chinese Mathematicians in 2013 for "his contributions to several fundamental problems in arithmetic geometry, algebraic groups, and representation theory".