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: 1. Undergraduate students   2. Graduate students

Teaching Language: English

Registration: https://www.wjx.top/vm/YAGstwp.aspx#