Arithmetic and Dynamics on Varieties of Markoff Type -Alexander Gamburd

Arithmetic Groups

Topic: Arithmetic and Dynamics on Varieties of Markoff Type
Speaker: Alexander Gamburd
Affiliation: The City University of New York
Date: April 13, 2022

The Markoff equation x2+y2+z2=3xyz, which arose in his spectacular thesis (1879), is ubiquitous in a tremendous variety of contexts. After reviewing some of these, we will discuss joint work with Bourgain and Sarnak establishing forms of strong approximation on varieties of Markoff type, as well as ensuing implications, diophantine and dynamical.