# Brandeis Dynamics and Number Theory Seminar 2019-2020

## Seminar Information

### Description

The Brandeis Dynamics and Number Theory Seminar is a research seminar broadly showcasing modern research in ergodic theory and dynamical systems, Lie theory, representation theory, geometry, and their interactions with number theory.

### Time and Location

Thursdays at 3:00PM in Goldsmith 226

## Schedule of Talks

### Fall 2019

September 12Dmitry KleinbockBrandeis UniversityShrinking targets in dynamics and number theoryLink to Abstract
September 19Lam PhamBrandeis UniversityExpansion spectral gaps in Lie groupsLink to Abstract
September 26Dmitry KleinbockBrandeis UniversityShrinking targets in number theory and dynamicsLink to Abstract
October 31Rahul KrishnaBrandeis UniversityTBALink to Abstract
November 7Byungchul ChaMuhlenberg CollegeTBALink to Abstract
November 21Jonathan JaquetteBrandeis UniversityWright’s Conjecture and the Prime Number TheoremLink to Abstract

## Detailed Abstracts

### September 12 @ 3:00PM – Dmitry Kleinbock (Brandeis) – Shrinking targets in dynamics and number theory

Abstract This is going to be an introduction to an active area of ergodic theory and dynamics, with applications to number theory. No background will be assumed, all are welcome.

### September 19 @ 3:00PM – Lam Pham (Brandeis) – Expansion and spectral gaps in Lie groups

Abstract I will survey recent results on various forms of expansion in groups. This is an old topic rooted in Lie theory and representation theory with many deep connections to number theory, geometry, dynamics, and even computing. I will present classical constructions due to Margulis, Kazhdan, and Lubotzky-Phillips-Sarnak and explain the breakthrough work of Bourgain and Gamburd on expansion in thin groups. Finally, I will present related works on improvements and generalizations of the Tits alternative and Kazhdan's Property $(T)$. The talk will be self-contained, with no background assumed.

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