# School of Mathematics

## Statistics for Families of Automorphic Representations

Let G be a connected reductive group over Q such that G(R) has discrete series representations. I will report on some statistical results on the Satake parameters (w.r.t. Sato-Tate distributions) and low-lying zeros of L-functions for families of automorphic representations of G(A). This is a joint work with Nicolas Templier.

## Automorphy: Automorphy Lifting Theorems I

## Automorphy: Deformations of Galois Representations (continued)

## Workshop on Topology

## Periodic Foams and Manifolds

WORKSHOP ON TOPOLOGY: IDENTIFYING ORDER IN COMPLEX SYSTEMS

## Grassmannians, Polytopes and Quantum Field Theory

WORKSHOP ON TOPOLOGY: IDENTIFYING ORDER IN COMPLEX SYSTEMS

## Topological Defects in Cosmology

WORKSHOP ON TOPOLOGY: IDENTIFYING ORDER IN COMPLEX SYSTEMS

## Does Infinite Cardinal Arithmetic Resemble Number Theory?

I will survey the development of modern infinite cardinal arithmetic, focusing mainly on S. Shelah's algebraic pcf theory, which was developed in the 1990s to provide upper bounds in infinite cardinal arithmetic and turned out to have applications in other fields.

This modern phase of the theory is marked by absolute theorems and rigid asymptotic structure, in contrast to the era following P. Cohen's discovery of forcing in 1963, during which infinite cardinal arithmetic was almost entirely composed of independence results.