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, January 6th 2025 (15:30-16:30, room A709)

Speaker: Martin J. Gander (Université de Genève)

Title: Landmarks in the History of Iterative Methods for Linear Systems

Abstract: Iterative methods for linear systems were invented for the same reasons as they are used today, namely to reduce computational cost. Gauss states in a letter to his friend Gerling in 1823: "you will in the future hardly eliminate directly, at least not when you have more than two unknowns". After a historical introduction to such classical stationary iterative methods, I will explain how the idea of extrapolation leads to Krylov methods, which are in fact not solvers but convergence accelerators. I will then introduce modern iterative methods for solving partial differential equations, which come in two main classes: domain decomposition methods and multigrid methods. These methods develop their full potential when used together with Krylov methods, namely as preconditioners.

Reference: Landmarks in the History of Iterative Methods, Martin J. Gander, Philippe Henry and Gerhard Wanner, SIAM Review, 2025

• December 2025 - Francis Bach (INRIA, ENS \& PSL). Denoising diffusion models without diffusions.
• November 2025 - Guillaume Barraquand (ENS Paris). Extreme diffusion.
• October 2025 - Agnès Desolneux (ENS Paris-Saclay). Mathematical Models for Texture Image Synthesis.
• June 2025 - Jessica Massetti (Università di Roma "Tor Vergata"). Recursive behaviors of Hamiltonian dynamical systems in finite and infinite dimension.
• May 2025 - Rupert Frank (Ludwig Maximilians Universität München). Sharp functional inequalities and their stability.
• April 2025 - Patricia Reynaud-Bouret (Université Côte d'Azur). Kalikow decomposition for the study of neuronal networks: simulation and learning (slides).
• March 2025 - Yilin Wang (IHES). The Brownian loop measure on Riemann surfaces and applications to length spectra.
• February 2025 - Anne-Laure Dalibard (Sorbonne Université). Stationary boundary layers in viscous incompressible fluids.
• January 2025 - Sylvia Serfaty (Sorbonne Université). Coulomb systems.
• December 2024 - Dorin Bucur (Université de Savoie). A free boundary approach of spectral optimization problems.
• 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.