Colloquium: Small points in arithmetic geometry and dynamical systems

Abstract: Height functions play a fundamental role in number theory, especially in counting and finiteness theorems as well as in the study of rational points on varieties. As a field that sets forth both analogues and generalizations of statements in Diophantine geometry, arithmetic dynamics has used heights as a major tool. Points of small canonical height are of particular interest, as they enjoy very distinctive arithmetic and geometric properties. In this talk, I will sketch a few seminal results concerning these points. As most of the progress in this area has so far occurred in the dimension 1 setting, I will discuss a recent result of mine transporting a key tool to the higher dimensional setting, with applications to small points on abelian varieties. 

Host: Wanlin Li

There will be a tea reception beforehand in Cupples I, Room 200 (Lounge) at 3:00 pm.