# Algebraic Geometry Seminar

#### Uniformity of Integral Points and Lang-Vojta'S Conjecture

**Speaker:**
Kenny Ascher, Brown University

**Location:**
Warren Weaver Hall 1314

**Date:**
Tuesday, November 1, 2016, 3:10 p.m.

**Synopsis:**

Caporaso, Harris, and Mazur proved, assuming Lang's conjecture, that the number of rational points on a smooth curve of genus greater than 1 is uniformly bounded by an integer depending solely on the genus and number field the curve is defined over. This theorem was proven by means of a purely algebro-geometric theorem known as a "fibered power theorem". We discuss how this uniformity result follows from the fibered power theorem, and discuss recent extensions (joint with A. Turchet) aiming to, assuming the Lang-Vojta conjecture, study uniformity results for integral points on curves and surfaces of log general type.