Colloque
Colloquium du CEREMADE
WANG Yilin (IHES)
Le 04/03/2025
De 15:30 à 16:30
Titre : The Brownian loop measure on Riemann surfaces and applications to length spectra
Résumé : The goal of this talk is to showcase how we can use stochastic processes to study the geometry of surfaces. More precisely, we use the Brownian loop measure to express the lengths of closed geodesics on a hyperbolic surface and zeta-regularized determinant of the Laplace-Beltrami operator. This gives a tool to study the length spectra of a hyperbolic surface and we obtain a new identity between the length spectrum of a compact surface and that of the same surface with an arbitrary number of additional cusps. This is based on a joint work with Yuhao Xue (IHES).
Salle : A709
Séminaire
Séminaire Analyse-Probabilités
JEGO Antoine (CNRS - Université Paris Dauphine)
Le 11/03/2025
De 10:30 à 11:30
Titre : Integration by parts in random conformal geometry
Résumé : Random objects satisfying a conformal invariance property naturally appear from the scaling limit of critical models of statistical mechanics. Examples include Schramm—Loewner Evolutions (SLE), the Gaussian free field (GFF), or even more classically, planar Brownian motion. In this talk, I will present our new approach to random conformal geometry based on the derivation of integration by parts formulas. I will in particular focus on two applications: our proof of the Kontsevich—Suhov conjecture and our new approach to random conformal weldings (Sheffield’s celebrated quantum zipper). Based on joint works with Guillaume Baverez.
Salle : Amphi 1
Séminaire
Séminaire Analyse-Probabilités
LACKER Daniel (Columbia University)
Le 18/03/2025
De 10:30 à 11:30
Titre : Projected Langevin dynamics and a gradient flow for entropic optimal transport
Résumé : The classical Langevin diffusion provides a natural algorithm for sampling from its invariant measure, which can be characterized as the unique minimizer of an energy functional over the space of probability measures. We introduce an analogous diffusion process that samples from an entropy-regularized optimal transport (a.k.a. Schrodinger bridge), which uniquely minimizes the same energy functional but constrained to the set of couplings of two given marginal probability measures. The law of the diffusion remains a coupling at each time if initialized as such. In addition, we show an exponential convergence rate by means of a new kind of logarithmic Sobolev inequality, in the case of sufficiently high temperature and (asymptotically) log-concave marginals. The dynamics can be viewed as a gradient flow on the space of couplings, viewed as a submanifold of Wasserstein space. Analogous constructions are possible for other constrained sampling problems, and as time permits I will discuss the surprisingly closely related example of mean field variational inference in Bayesian statistics.
Salle : A711
Séminaire
Séminaire Analyse-Probabilités
ARCHER Eleanor (Ceremade - Université Paris Dauphine PSL)
Le 25/03/2025
De 10:30 à 11:30
Titre : TBA
Résumé : TBA
Salle : A709
Colloque
Colloquium du CEREMADE
REYNAUD-BOURET Patricia (Université Côte d'Azur)
Le 01/04/2025
De 15:30 à 16:30
Titre : Kalikow decomposition for the study of neuronal networks: simulation and learning
Résumé : Kalikow decomposition is a decomposition of stochastic processes (usually finite state discrete time processes but also more recently point processes) that consists in picking at random a finite neighborhood in the past and then make a transition in a Markov manner. This kind of approach has been used for many years to prove existence of some processes, especially their stationary distribution. In particular, it allows to prove the existence of processes that model infinite neuronal networks, such as Hawkes like processes or Galvès-Löcherbach processes. But beyond mere existence, this decomposition is a wonderful tool to simulate such network, as an open physical system, that from a computational point of view could be competitive with the most performant brain simulations. This decomposition is also a source of inspiration to understand how local rules at each neuron can make the whole network learn.
Salle : A709
Séminaire
Séminaire Analyse-Probabilités
AYI Nathalie (LJLL)
Le 29/04/2025
De 10:30 à 11:30
Titre : TBA
Résumé :
Salle : A711
Séminaire
Séminaire Analyse-Probabilités
DEMBIN Barbara (Université de Strasbourg)
Le 13/05/2025
De 10:30 à 11:30
Titre : TBA
Résumé :
Salle : A711
Séminaire
Séminaire Analyse-Probabilités
GLOGIC Irfan (Bielefeld University)
Le 20/05/2025
De 10:30 à 11:30
Titre : TBA
Résumé : TBA
Salle : A711
Séminaire
Séminaire Analyse-Probabilités
SCHAPIRA Barbara (Université de Montpellier)
Le 27/05/2025
De 10:30 à 11:30
Titre : TBA
Résumé :
Salle : A711