# Kinetic Theory Seminar for women in math

### 27 Apr 2024

We are pleased to announce the "Kinetic Theory Seminar for women in math”.

This seminar series brings together researchers interested in kinetic theory from the Zurich and Basel area. There will be one event per semester, alternating locations between the ETH Zurich and the University of Basel.

The next edition will celebrate the achievements of women in the field in the framework of the May12 initiative

**Date: **Thursday, 16th May 2024

**Time: **2:15 p.m. – 5:00 p.m. 2:15 - 3:15 First talk and discussions.

3:15 - 4:00 Coffee Break

4:00 – 5:00 Second talk and discussions.

**Room:** ETH Zurich, HG E5 (Rämistrasse 101, 8092 Zürich)

(coffee break: Foyer HG E-Süd)

**Speakers: **

Prof. Alessia Nota (Università degli studi dell’Aquila)

**Title: **Recent advances on the Smoluchowski coagulation equation under non-equilibrium conditions

**Abstract: **In this talk I will first discuss some fundamental properties of the Smoluchowski’s coagulation equation, an integro-differential equation of kinetic type, which provides a mean-field description for mass aggregation phenomena. I will then present some recent results on the problem of existence or non-existence of stationary solutions, both for single and multi-component systems, under non-equilibrium conditions which are induced by the addition of a source term for small cluster sizes. The most striking feature of these stationary solutions is that, whenever they exist, the solutions to multi-component systems exhibit an unusual “spontaneous localization” phenomenon: they localize along a line in the composition space as the total size of the particles increase. This localization is a universal property of multicomponent systems and it has also been recently proved to occur in time dependent solutions to mass conserving coagulation equations.
(Based on joint works with M.Ferreira, J.Lukkarinen and J. Velázquez)

Prof. Nathalie Ayi (Sorbonne University)

**Title:** Large Population Limit for Interaction Particle Systems on Weighted Graphs

**Abstract: **When studying interacting particle systems, two distinct categories emerge: indistinguishable systems, where particle identity does not influence system dynamics, and non-exchangeable systems, where particle identity plays a significant role. One way to conceptualize these second systems is to see them as particle systems on weighted graphs. In this talk, we focus on the latter category. Recent developments in graph theory have raised renewed interest in understanding large population limits in these systems. Two main approaches have emerged: graph limits and mean-field limits. While mean-field limits were traditionally introduced for indistinguishable particles, they have been extended to the case of non-exchangeable particles recently. In this presentation, we introduce several models, mainly from the field of opinion dynamics, for which rigorous convergence results as N tends to infinity have been obtained. We also clarify the connection between the graph limit approach and the mean-field limit one. The works discussed draw from several papers, some co-authored with Nastassia Pouradier Duteil and David Poyato.