Arithmetic and dynamics on varieties of Markoff type
Alexander Gamburd
The Graduate Center, CUNY, New York, NY, USA
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Abstract
The Markoff equation , which arose in his spectacular thesis in 1879, is ubiquitous in a tremendous variety of contexts. After reviewing some of these, we discuss Hasse principle, asymptotics of integer points, and, in particular, recent progress towards establishing forms of strong approximation on varieties of Markoff type, as well as ensuing implications, diophantine and dynamical.