Peter Hintz and Sarah Zerbes at ICM 2022
From 6 to 14 July 2022, the International Congress of Mathematicians 2022 (ICM 2022) will take place. The Department is represented by two speakers and is organizing an ICM sectional workshop on number theory and algebraic geometry.
Sectional speakers
Sarah Zerbes (co-speaker David Loeffler)
Friday, 8 July 2022, 3.15–4.00 p.m.
Euler systems and the Bloch-Kato conjecture for automorphic Galois representations
Abstract: The Bloch–Kato conjecture is a very general conjecture relating special values of L-functions to Selmer groups of Galois representations, generalising many earlier results and conjectures such as the Birch–Swinnerton-Dyer conjecture for elliptic curves. One of the most powerful tools available for attacking this conjecture is the theory of Euler systems, which are certain compatible families of cohomology classes which serve to bound the sizes of Selmer groups. In a series of recent works (variously joint with Lei, Pilloni, and Skinner), we have made new breakthroughs in the construction of Euler systems, combining the geometry of Shimura varieties with the representation theory of spherical pairs over local fields; and developed new techniques for proving explicit reciprocity laws, relating Euler systems to critical values of L-functions. We recently used these techniques to prove the Bloch–Kato conjecture in analytic rank 0 for critical values of the degree 4 L-function of GSp(4), and hence obtain new results towards the Birch–Swinnerton-Dyer conjecture for modular abelian surfaces. We will describe this result and work in progress to generalise it to a range of other automorphic L-functions.
Peter Hintz (co-speaker Gustav Holzegel)
Sunday, 10 July, 1.15–2:00 p.m.
Recent Progress in General Relativity
Abstract: We review recent progress in general relativity. After a brief introduction to some of the key analytical and geometric features of the Einstein equations, we focus on two main developments: the stability of black hole solutions, and the formation, structure, and dynamical stability of singularities.
ICM overlay event
Although external pageICM 2022 takes place virtually, there are so-called overlay events that complement the core programme, take place in the presence of an audience and are then recorded or streamed live. The Department is organizing such an in-person workshop to cover sections 3 (Number Theory) and 4 (Algebraic and Complex Geometry):
ICM Sectional Workshop Number Theory and Algebraic Geometry
11–14 July 2022
Organised by Bruno Klingler (HU Berlin), Emmanuel Kowalski (D-MATH), David Loeffler (Warwick), Sarah Zerbes (D-MATH).