Our colloquium takes place on the first Tuesday of each month from 15:30 to 16:30, usually in room **A709**.

A renowned expert (being an excellent speaker as well) visits us for an afternoon and gives a panorama of one of her research areas. The talk is meant to be accessible to all members of the lab, including PhD students in analysis, game theory, probability and statistics. Ideally, it should start gently with an historical background on the problem and an overview of the main questions and applications, keeping a non technical style during at least the first half of the talk. Of course it is also nice to have a part with more mathematical details: the most appreciated colloquia were those in which the speaker succeeded to develop a nice technical idea or an elegant argument that everyone should know.

Food and drinks are served after the event, usually in **Espace 7**!

If you know good speakers whom you would love to hear, do not hesitate to suggest their names to the two organizers: and .

**Date**: Tuesday, June 4th 2024 (15:30-16:30, room C206)

**Speaker**: (Université de Lille)

**Title**: Mathematical aspects of 2D Yang-Mills theory

**Abstract**: In the fifties, Chen Ning Yang and Robert Mills made a major breakthrough in quantum field theory by extending the concept of gauge theory to non-abelian groups. Since then, the study of Yang-Mills theory has been a very active field of research both in mathematics and physics, in various directions. In particular, the theory on two-dimensional manifolds with gauge group U(N) or SU(N) has been studied as an (already very interesting) toy model, first by physicists in the nineties and then by mathematicians in the last two decades. If this talk, I will give an overview of the main mathematical results in this direction. Hopefully, if time allows, I will also explain in more details how the probabilistic study of well chosen random partitions allows us to give a reasonably simple rigorous proof of some topological expansions of the partition function of 2D Yang-Mills, predicted by physicists Gross and Taylor in the nineties (joint work with Thibaut Lemoine, Université de Lille).

- May 2024 - (Université Lyon 1).
*Euclidean, metric, and Wasserstein gradient flows.* - April 2024 - (University of Bristol and Alfréd Rényi Institute of Mathematics).
*The Random Lorentz Gas.* - March 2024 - (Sorbonne Université).
*A tale of heavy tails.* - February 2024 - (École polytechnique).
*Utilisation de modèles d'ordre réduit pour l'imagerie par ondes.* - December 2023 - (Università Roma Tre).
*Navigating Networks by Random Walks.* - November 2023 - (Université Paris-Saclay).
*Sciences sociales et flots de gradient.* - October 2023 - (INRIA).
*Mathématiques et Intelligence Artificielle.* - June 2023 - (NYUAD).
*Phenomena in High Dimensions.* - April 2023 - (Université de Strasbourg).
*Principes d'incertitude, inégalités d'incertitude.* - January 2023 - (Ecole Polytechnique).
*Autour de la modélisation statistique par les processus de Hawkes.* - December 2022 - (University of Bath).
*Random growth processes: dendritic formation and competition.* - October 2022 - (Universidad de Chile).
*Solitary waves in non-linear Dirac equations.* - May 2022 - (Georgia Institute of Technology).
*Optimal criteria for magnetic fields that bind electrons.* - April 2022 - (Ecole Normale Supérieure de Paris).
*Sur la dynamique des gaz dilués.* - December 2021 - (Université Paris-Saclay).
*Quand la dépendance ouvre des possibles.* - October 2021 - (Université Paris-Saclay).
*Surfaces aléatoires en tous genres.*