Jun 15, 2023
Arithmetic and Dynamics on Varieties of Markoff Type
Algebraic Geometry and Number Theory Seminar
Date: June 15, 2023 |
1:00 pm –
3:00 pm
Speaker:
Alexander Gamburd, The Graduate Center, CUNY
Location: Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Language:
English
The Markoff equation $x^2+y^2+z^2=3xyz$, which arose in his spectacular thesis (1879), is ubiquitous in a tremendous 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.