Lie Groups, Dynamics and Number Theory

Speaker：Han Li 李涵

Wesleyan University

Han Li's research interest lies in Lie groups, discrete subgroups, dynamics on homogenous spaces and their interactions with number theory and geometry. He received his PhD degree in Mathematics from Yale University in 2014. Prior to joining Wesleyan he spent an academic year as a postdoc at the University of Texas at Austin and MSRI Berkeley.

Time

Tues. & Thur., 13:30-15:05,

May 13-June 5, 2025

Venue

B534, Shuangqing Complex Building A

Description

The study of dynamics on homogeneous spaces of Lie groups has emerged as a distinct and rapidly evolving field, integrating research areas such as ergodic theory, geometry, and number theory.

This course explores homogeneous dynamics and its applications to number theory, covering the following topics:

1.Introduction to homogeneous dynamics – An overview of the subject and its significance.

2.Ergodicity, mixing, and equidistribution.

3.Farey fractions, geometry of numbers, and connections to homogeneous dynamics.

4.Recurrence in homogeneous spaces and reduction theory of quadratic forms.

5.Arithmetic groups, spectral gaps, and the rate of mixing.

6.Homogeneous dynamics in number theoretic problems: search bounds of equivalence of integral quadratic.

This course aims to provide both foundational insights and advanced techniques at the intersection of these mathematical disciplines.

Prerequisite:

First year graduate level analysis, algebra and topology

Target Audience:

Undergraduate students

Graduate students

Teaching Language: English