# Plenary and public lectures

## Plenary lectures

Artur Avila, Universität Zürich, Switzerland & IMPA, Brazil

Date: 2019-09-20 (Friday); Time: 16:20-17:20; Location: building U-2, auditorium.

Abstract

Alessio Figalli, ETH Zürich, Switzerland

Date: 2019-09-18 (Wednesday); Time: 09:00-10:00; Location: building U-2, auditorium.

Abstract

Stable solutions to semilinear elliptic PDEs appear in several problems. It is known since the 1970’s that, in dimension $$n \gt 9$$, there exist singular stable solutions. In this talk I will describe a recent work with Cabré, Ros-Oton, and Serra, where we prove that stable solutions in dimension $$n \le 9$$ are smooth. This answers also a famous open problem, posed by Brezis, concerning the regularity of extremal solutions to the Gelfand problem.

Martin Hairer, Imperial College London, UK

Date: 2019-09-19 (Thursday); Time: 09:00-10:00; Location: building U-2, auditorium.

Abstract

Stanislav Smirnov, University of Geneva, Switzerland & Skoltech, Russia

Joint work with Mikhail Khristoforov

Date: 2019-09-17 (Tuesday); Time: 09:00-10:00; Location: building U-2, auditorium.

Abstract

We will discuss the state of our understanding of 2D percolation, and will present a recent joint work with Mikhail Khristoforov, giving a new proof of its conformal invariance at criticality.

Shing-Tung Yau, Harvard University, USA

Date: 2019-09-16 (Monday); Time: 09:00-10:00; Location: building U-2, auditorium.

Abstract

I shall give a talk about a joint work that I did with Tristan Collins on an important nonlinear system equation of Monge-Ampère type. It is motivated from the theory of Mirror symmetry in string theory. I shall also talk about its algebraic geometric meaning.

Maciej Zworski, University of California, Berkeley, USA

Date: 2019-09-20 (Friday); Time: 09:00-10:00; Location: building U-2, auditorium.

Abstract

Microlocal analysis exploits mathematical manifestations of the classical/quantum (particle/wave) correspondence and has been a successful tool in spectral theory and partial differential equations. We can say that these two fields lie on the "quantum/wave side".

In the last few years microlocal methods have been applied to the study of classical dynamical problems, in particular of chaotic flows. That followed the introduction of specially tailored spaces by Blank-Keller-Liverani, Baladi-Tsujii and other dynamicists and their microlocal interpretation by Faure-Sjoestrand and by Dyatlov and the speaker.

I will explain this microcar/dynamical connection in the context of Ruelle resonances, decay of correlations and meromorphy of dynamical zeta functions. I will also present some recent advances, among them results by Dyatlov-Guillarmou (Smale's conjecture on meromorphy of zeta functions for Axiom A flows), Guillarmou-Lefeuvres (local determination of metrics by the length spectrum) and Dang-Rivière (Ruelle resonances and Witten Laplacian).

## Public lecture

Alessio Figalli, ETH Zürich, Switzerland

Date: 2019-09-18 (Wednesday); Time: 13:30-14:30; Location: building U-2, auditorium.

Abstract

In this talk I'll give a general overview, accessible also to non-specialists, of the optimal transport problem. Then I'll show some applications of this theory to soap bubbles (isoperimetric inequalities) and clouds (semigeostrophic equations), problems on which I worked over the last 10 years. Finally, I will conclude with a brief description of some results that I recently obtained on the study of ice melting into water.