Institut de recherche mathématique avancée

Résumé : Le processus de Fleming-Viot est un système de particule en interaction de type champ moyen. Lorsque le nombre de particule tends vers l'infini, la mesure empirique au temps t>0 d'un tel système est un estimateur de la loi d'un processus de Markov, conditionné à sa survie (en un sens que l'on définira). Dans cette exposé, je présenterai la preuve de la convergence uniforme en temps du processus de Fleming-Viot, dans le cas d'une mort douce, possiblement non-bornée, vers cette loi conditionnée. Cet exposé sera basé sur un travail en collaboration avec Mathias Rousset de l'INRIA Rennes.

Résumé : Electronic structure calculations are widely used to predict the physical properties of molecules and materials. They require to solve nonlinear partial differential and eigenvalue equations. These equations are generally numerically very demanding, especially since they are parameterized by the positions of the nuclei in the molecule and must be solved a large number of times when these positions vary. This is the case for example when simulating the dynamics of a molecule. In this talk, I will present a recent work aimed at efficiently calculating approximate solutions of such parameterized PDEs, with the objective of reducing the overall computational time. For this, I will present a non-linear interpolation method between several solutions, based on optimal transport, and using in particular Wasserstein barycenters. I will illustrate this method with simulations carried out on a 1D toy model.

Résumé : Je vais parler du progrès récent dans l'étude des espaces de modules des faisceaux cohérents sur les surfaces algébriques lisses, notamment de la preuve de la conjecture P=W de de Cataldo-Hausel-Migliorini, que je vais introduire et motiver. Le cœur technique sera le calcul explicite de l'action de certains opérateurs d'Hecke sur l'homologie de ces espaces de modules.

Résumé : Since its inception in 2008 as the underlying technology behind Bitcoin, blockchain has evolved far beyond its cryptocurrency origins. Over the past decade, various blockchain systems have emerged, demonstrating diverse applications across industries. This talk provides a quick dive into blockchain analysis. I will cover the essentials of blockchain technology with a focus on consensus protocols like proof-of-work and proof-of-stake before discussing some applications in Finance and Insurance.

The seminar will take place in the Amphithéâtre du Bâtiment de la Grande Coupole, opposite the entrance at 11 rue de l'Université. It will be also broadcasted via BBB: https://bbb.unistra.fr/b/hum-51d-suf-mzq

Pierre-Olivier Goffard is an Associate Professor at the University of Strasbourg, France. He conducts research at the intersection of applied probability, statistics, and their applications in finance and insurance. His areas of expertise encompass blockchain technology and Bayesian statistics. Pierre-Olivier actively participates in the actuarial science program at the University of Strasbourg, where he teaches courses on stochastic calculus and survival analysis.