What's Happening in Fine Hall

Elliptic curves are fundamental and well-studied objects in arithmetic geometry. However, much is still not known about many simple-sounding properties, such as the expected number of rational or integral points on a "random" elliptic curve. We will briefly discuss some conjectures and theorems related to these problems. In particular, we will show why the second moment (and the average) for the number of integral points on elliptic curves over a number field is bounded (joint work with Levent Alpöge).

This talk will be suitable for a general mathematical audience.