## Space-time correlations at equilibrium

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

Laure Saint-Raymond

University Paris VI Pierre et Marie Curie and Ecole Normale Supérieure

April 9, 2019

Although the distribution of hard spheres remains essentially chaotic in this regime, collisions give birth to small correlations. The structure of these dynamical correlations is amazing, going through all scales.

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

Renato Bettiol

City University of New York

April 9, 2019

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.

Hamed Hatami

University of McGill

April 8, 2019

The seminal result of Kahn, Kalai and Linial implies that a coalition of a small number of players can bias the outcome of a Boolean function with respect to the uniform measure. We extend this result to arbitrary product measures, by combining their argument with a completely different argument that handles very biased coordinates.

Laure Saint-Raymond

University Paris VI Pierre et Marie Curie and Ecole Normale Supérieure

April 8, 2019

Consider a system of small hard spheres, which are initially (almost) independent and identically distributed.

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?

Oleg Lazarev

Columbia University

April 8, 2019

Jian Ding

The Wharton School, The University of Pennsylvania

April 5, 2019

I will discuss random field Ising model on $Z^2$ where the external field is given by i.i.d. Gaussian

variables with mean zero and positive variance. I will present a recent result that at zero temperature the effect of boundary conditions on the magnetization in a finite box decays exponentially in the distance to the boundary. This is based on joint work with Jiaming Xia.

variables with mean zero and positive variance. I will present a recent result that at zero temperature the effect of boundary conditions on the magnetization in a finite box decays exponentially in the distance to the boundary. This is based on joint work with Jiaming Xia.

Yash Jhaveri

Member, School of Mathematics

April 4, 2019

In this talk, I will give an overview of some of what is known about solutions to the thin obstacle problem, and then move on to a discussion of a higher regularity result on the singular part of the free boundary. This is joint work with Xavier Fernández-Real.

Jan Vonk

Oxford University

April 4, 2019

The theory of complex multiplication describes finite abelian extensions of imaginary quadratic number fields using singular moduli, which are special values of modular functions at CM points. I will describe joint work with Henri Darmon in the setting of real quadratic fields, where we construct p-adic analogues of singular moduli through classes of rigid meromorphic cocycles. I will discuss p-adic counterparts for our proposed RM invariants of classical relations between singular moduli and analytic families of Eisenstein series.

Stephen Kotkin

Princeton University

April 4, 2019

Minhyong Kim

Oxford University

April 3, 2019