## How does the rank of an elliptic curve grow in towers of number fields?

## Loops in hydrodynamic turbulence

## On the possibility of an instance-based complexity theory.

## Etale and crystalline companions

Deligne's "Weil II" paper includes a far-reaching conjecture to the

effect that for a smooth variety on a finite field of characteristic p,

for any prime l distinct from p, l-adic representations of the etale

fundamental group do not occur in isolation: they always exist in

compatible families that vary across l, including a somewhat more

mysterious counterpart for l=p (the "petit camarade cristallin"). We

explain in more detail what this all means, indicate some key

## Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK

## Reinterpreting Political Violence in 20th-Century Europe: A Comparative Perspective

## Fluctuations look like white noise

They actually satisfy a stochastic PDE with time-space white noise.

Can we say more using higher order cumulants?

## The energy functional on Besse manifolds

A Riemannian manifold is called Besse, if all of its geodesics are periodic. The goal of this talk is to study the energy functional on the free loop space of a Besse manifold. In particular, we show that this is a perfect Morse-Bott function for the rational, relative, S1-equivariant cohomology of the free loop space. We will show how this result is crucial in proving a conjecture of Berger for spheres of dimension at least 4, although it might be useful for proving the conjecture in full generality.

## Space-time correlations at equilibrium

How combinatorial techniques can help to analyze this departure from chaos?