Speaker: Rob Rockwood (14:00)

Title: Arithmetic applications of spherical varieties

Abstract: We discuss how the theory of spherical varieties can be applied to study p-adic variation of cohomology classes and how these can be applied to prove new cases of the Birch—Swinnerton-Dyer conjecture for abelian surfaces.

Speaker: Oliver McGrath (14:30)

Title: Applications of sieves

Abstract: We look at some applications of sieve methods in analytic number theory. In particular, we will look at how sieves can be used to detect patterns in prime numbers and, if there is time, how sieves can be used to count solutions to Diophantine equations.