## Number Theory Seminar

### Thursday, November 14th, 2019

**Time:** 4:30-5:30 p.m. **Place:** Jeffery Hall 422

**Speaker:** Mike Roth (Queen's University)

**Title:** A measure of positivity of a line bundle along a subschemes, and a simpler proof of the Ru-Vojta arithmetic theorem.

**Abstract:** Diophantine geometry seeks to link properties of rational solutions of a set of equations to the geometric properties of the variety they define. One of the main tools in Diophantine geometry is Diophantine approximation — results bounding how the complexity of a rational point must grow as it approaches a subvariety. In this talk I will discuss a somewhat recent new measure of the positivity of an ample line bundle along a subscheme, and show how its formal properties give a simple proof of a theorem of Ru-Vojta on Diophantine approximation. This is joint work with David McKinnon at Waterloo.