Arithmetic and Dynamics on Varieties of Markoff Type
Algebraic Geometry and Number Theory Seminar
Date:
Thursday, June 15, 2023 13:00 - 15:00
Speaker:
Alexander Gamburd (The Graduate Center, CUNY)
Location:
Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Series:
Mathematics and CS Seminar
Host:
Tim Browning
Contact:
Birgit Oosthuizen-Noczil
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.