# Overview

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## Isabelle Gallagher Aisenstadt Chair Lecture Series

Isabelle Gallagher will give a series of three lectures when she comes to the Centre de recherches mathématiques for the Aisenstadt Chair.

The presentations will take place in the workshop: Unifying concepts in PDEs with randomness in May 2022.

**First lecture :
**

**Monday, May 16, 2022, 2 p.m.**

Centre de recherches mathématiques

André-Aisensdadt Pavilion, Université de Montréal

Room 6214/6254

**Second lecture: **

**Tuesday, May 17, 2022, 2:00 p.m. **

Centre de recherches mathématiques

André-Aisensdadt Pavilion, Université de Montréal

Room 6214/6254

**Title**: Mathematical analysis of dilute gases : derivation of the Boltzmann equation, fluctuations and large deviations

**Abstract:**

In these two lectures I will present some recent advances and open problems related to a statistical approach to the mathematical analysis of dilute gases: the focus will be on fluctuations and large deviations around the Boltzmann equation.

**Third lecture (intended for a broader audience):**

**Friday, May 20, 2022, 3:30 p.m. (on Zoom and on site)**

Centre de recherches mathématiques

André-Aisensdadt Pavilion, Université de Montréal

Room 6214/6254

**(To get the Zoom link if you are not a participant of the March 14-25 workshop, please register ****here****)**

**Title**: Mathematical analysis of dilute gases : derivation of the Boltzmann equation, fluctuations and large deviations

**Abstract:**

The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied gases, it is expected that continuum laws of kinetic theory can be obtained directly from molecular dynamics governed by the fundamental principles of mechanics. In the case of hard sphere gases, Lanford showed in 1975 that the Boltzmann equation emerges as the law of large numbers in the low density limit, at least for very short times. The goal of this talk is to explain the heuristics of his proof and present recent progress in the understanding of this limiting process.

**Biography:**

Isabelle Gallagher is a French mathematician. Her research concerns partial differential equations such as the Navier-Stokes equations, wave equation, and Schrödinger equation, as well as harmonic analysis of the Heisenberg group.

She earned her Ph.D. from Pierre and Marie Curie University in 1998. Her dissertation, supervised by Jean-Yves Chemin, concerned fluid dynamics.

From 1998 to 2001, she was a research fellow at Paris-Sud University; From 2001 to 2004, she joined the Laurent Schwartz Mathematics Center at the École polytechnique, then in 2004 became a professor at the University of Paris-Diderot. In 2018 and 2019, she directed the Department of Mathematics and Applications at the École Normale Supérieure (Paris).

Since 2019, she has been director of the Fondation Sciences Mathématiques de Paris.

She won the CNRS Silver Medal in 2016.