The Ruth Moufang Lectures will have their second iteration on July 13th and 14th, 2023 in Darmstadt. We are happy to announce that our speaker will be Sarah Zerbes (ETH Zürich). The lectures will circle around the BSD conjecture and Euler systems.

Sarah Zerbes – An introduction to the theory of Euler systems
Abstract: Euler systems are one of the most powerful tools for proving new cases of the Birch–Swinnerton-Dyer and Bloch–Kato conjectures. In my lectures, I will give an introduction to the theory of Euler systems, and give some examples of how to construct and where to find them.

• 3rd lecture: Euler systems and the BSD conjecture for abelian surfaces

Abstract:

I will recall a series of recent works (variously joint with Loeffler, Pilloni, Skinner) giving rise to an Euler system in the cohomology of Shimura varieties for GSp(4), and an explicit reciprocity law relating the Euler system to values of L-functions. I will then explain recent work with Loeffler, where we use this Euler system to prove new cases of the BSD conjecture for modular abelian surfaces over Q, and for modular elliptic curves over imaginary quadratic fields.

Lectures 2 and 3 are aimed at mathematicians with a background in number theory.