Departmental Colloquium
Wei Ho
University of Michigan
Integral points on elliptic curves
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).
Following the talk, there will be tea in SEO 300.
Friday September 27, 2019 at 3:00 PM in 636 SEO