Special Colloquium
Aaron Levin
Michigan State University
Points of bounded degree on curves
Abstract: A central problem in number theory is to determine the set of solutions in integers to a system of polynomial equations. When the system of equations geometrically defines an affine curve, a fundamental result of Siegel yields the finiteness of integral solutions if either the curve has positive genus or the curve has more than two points at infinity. We will give a generalization of Siegel's theorem to integral points of degree d, resulting in a complete characterization of affine curves with infinitely many integral points of degree d (over some number field). We will also briefly discuss the connection with Picard's theorem in complex analysis and analogous results in that setting.
There is a Meet & Greet Tea right after the talk in SEO 300.
Thursday January 22, 2015 at 3:00 PM in SEO 636