Monday, October 28, 2019
Time  Items 

All day 

4pm 
10/28/2019  4:00pm Abstract: Elliptic curves are fundamental and wellstudied 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). Location:
LOM 206

5pm 
10/28/2019  5:15pm Abstract: Integration of differential forms against cycles on a complex manifold helps relate de Rham cohomology to singular cohomology, which forms the beginning of Hodge theory. The analogous story for padic manifolds, which is the subject of padic Hodge theory, is richer due to a wider variety of available cohomology theories (de Rham, etale, crystalline, and more) and torsion phenomena. In this talk, I will give a bird’s eye view of this picture, guided by the recently discovered notion of prismatic cohomology (which was inspired by calculations in homotopy theory) that provides some cohesion to the story. Based on joint works with Morrow and Scholze. Location:
LOM 206
