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Wednesday Feb. 18, 2015

Jason Bell, University of Waterloo

Applications of p-adic analysis to algebra and geometry

**Abstract**:

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We consider some recent applications of techniques of p-adic analysis to
algebra and geometry. Specifically, we consider three applications. First, we show that it gives a solution to a
problem of Keeler, Rogalski, and Stafford asking to show that if the orbit
of a point under an automorphism of a complex projective variety has the
property that it intersects some subvariety infinitely often then the orbit
cannot be Zariski dense. Next, we show that one can give a new proof of a
result of Bass and Lubotzky showing that the Burnside problem has an
affirmative solution for automorphism groups of quasiprojective varieties.
Finally, we consider an application that gives a result of Bogomolov and
Tschinkel: a K3 surface defined over a number field F with an infinite
automorphism group has a dense set of K-points for some finite extension
of F. This includes joint work with Dragos Ghioca, Zinovy Reichstein,
Daniel Rogalski, Sue Sierra, and Tom Tucker.