Integral points on elliptic curves

Seminar: 
Colloquium
Event time: 
Monday, October 28, 2019 - 4:00pm
Location: 
LOM 206
Speaker: 
Wei Ho
Speaker affiliation: 
University of Michigan
Event description: 

Abstract: Elliptic curves are fundamental and well-studied objects in arithmetic geometry. However, much is still not known about many basic properties, such as the number of rational points on a “random” elliptic curve. We will discuss some conjectures and theorems about this “arithmetic statistics” problem, and then show how they can be applied to answer a related question about the number of integral points on elliptic curves over Q. In particular, we show that the second moment (and the average) for the number of integral points on elliptic curves over Q is bounded (joint work with Levent Alpoge).