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: Justin Salez and Cristina Toninelli.

Date: Tuesday, December 3rd 2024 (15:30-16:30, room D207)

Speaker: Dorin Bucur (Université de Savoie)

Title: A free boundary approach of spectral optimization problems

Abstract: Why all the drums are round! This assertion is mathematically rephrased as follows: among all membranes with prescribed area, the one producing the lowest fundamental frequency has a circular shape. But what about the shapes of membranes with higher extremal frequencies? The general question in which are are interested concerns the relationship between the geometry of the domain and the spectrum of a differential operator defined on this domain. In this talk I will focus on the Neumann eigenvalues of the Laplace operator on domains of Euclidean space and on spheres. Together with a discussion about existence/non existence of optimal geometries and possible relaxation on densities, I will give some numerical approximations of the best geometries and densities. A particular attention will be given to the lowest two non trivial eigenvalues for which a full answer is given in any dimension of the Euclidean space. A surprising phenomenon occurs on spheres: while a complete answer can be given for the second eigenvalue, for the first one an unexplained phenomenon occurs. The results presented in this talk have been obtained in series of collaborations with R. Laugesen, A. Henrot, E. Martinet, M. Nahon and E. Oudet.

• November 2024 - Céline Duval (Sorbonne Université). Geometry of excursion sets: Computing the surface area from discretized points.
• October 2024 - Thierry Bodineau (IHES). A renormalisation group perspective on functional inequalities.
• June 2024 - Mylène Maïda (Université de Lille). Mathematical aspects of 2D Yang-Mills theory.
• May 2024 - Filippo Santambrogio (Université Lyon 1). Euclidean, metric, and Wasserstein gradient flows.
• April 2024 - Bálint Tóth (University of Bristol and Alfréd Rényi Institute of Mathematics). The Random Lorentz Gas.
• March 2024 - Ismaël Castillo (Sorbonne Université). A tale of heavy tails.
• February 2024 - Josselin Garnier (École polytechnique). Utilisation de modèles d'ordre réduit pour l'imagerie par ondes.
• December 2023 - Pietro Caputo (Università Roma Tre). Navigating Networks by Random Walks.
• November 2023 - Bertrand Maury (Université Paris-Saclay). Sciences sociales et flots de gradient.
• October 2023 - Marc Lelarge (INRIA). Mathématiques et Intelligence Artificielle.
• June 2023 - Pierre Youssef (NYUAD). Phenomena in High Dimensions.
• April 2023 - Nalini Anantharaman (Université de Strasbourg). Principes d'incertitude, inégalités d'incertitude.
• January 2023 - Mathieu Rosenbaum (Ecole Polytechnique). Autour de la modélisation statistique par les processus de Hawkes.
• December 2022 - Alexandre Stauffer (University of Bath). Random growth processes: dendritic formation and competition.
• October 2022 - Hanne Van Den Bosch (Universidad de Chile). Solitary waves in non-linear Dirac equations.
• May 2022 - Michael Loss (Georgia Institute of Technology). Optimal criteria for magnetic fields that bind electrons.
• April 2022 - Isabelle Gallagher (Ecole Normale Supérieure de Paris). Sur la dynamique des gaz dilués.
• December 2021 - Elisabeth Gassiat (Université Paris-Saclay). Quand la dépendance ouvre des possibles.
• October 2021 - Nicolas Curien (Université Paris-Saclay). Surfaces aléatoires en tous genres.