Speaker: Alex Gamburd (CUNY Graduate Center)

Title: Arithmetic and dynamics on varieties of Markoff type

Abstract:

The Markoff equation $x^2+y^2+z^2=3xyz$, which arose in his spectacular thesis (1879), is ubiquitous in a wide variety of contexts. After reviewing some of these, we will discuss (briefly) asymptotics of integer points, and (in some detail) recent progress towards establishing forms of strong approximation on varieties of Markoff type, as well as ensuing implications, diophantine and dynamical.