## 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?

## Bifurcating conformal metrics with constant Q-curvature

The problem of finding metrics with constant Q-curvature in a prescribed conformal class is an important fourth-order cousin of the Yamabe problem. In this talk, I will explain how certain variational bifurcation techniques used to prove non-uniqueness of solutions to the Yamabe problem also yield non-uniqueness results for the constant Q-curvature problem. However, special emphasis will be given to the differences between multiplicity phenomena in these two variational problems. This is based on joint work with P. Piccione and Y. Sire.

## Collective Coin-Flipping Protocols and Influences of Coalitions

## Disorder increases almost surely.

Then, in the low density limit, their empirical measure $\frac1N \sum_{i=1}^N \delta_{x_i(t), v_i(t)}$ converges

almost surely to a non reversible dynamics.

Where is the missing information to go backwards?