There is a natural dichotomy between telescopic(T(n)-local) and chromatic (K(n)-local) homotopy theory. Telescopic homotopy theory is more closely tied to the stable homotopy groups of spheres and through them to geometric questions, but is generally computationally intractable. Chromatic homotopy theory is more closely tied to arithmetic geometry and powerful computational tools exist in this setting. Ravenel’s telescope conjecture asserted that these two sides coincide. I will present a family of counterexamples to this conjecture based on using trace methods to analyze the algebraic K-theory of a family of K(n)-local ring spectra beginning with the K(1)-local sphere. As a consequence of this we obtain a new lower bound on the average rank of the stable homotopy groups of spheres. I will then describe the étale fundamental group of the T(n)-local sphere and how this informs our understanding of telescopic homotopy theory. This talk is based on projects joint with Carmeli, Clausen, Hahn, Levy, Schlank and Yanovski. Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide. 

11e séminaire ITZYKSON :Dénombrement de cartes : entre combinatoire, probabilités et physique théoriqueLe 11e séminaire Itzykson est organisé par Maxim Kontsevich (IHES), Sylvain Ribault (IPhT Saclay) et Pierre Vanhove (IPhT Saclay). Depuis une dizaine d’années l’axe math-physique de la Fondation Mathématique Jacques Hadamard (FMJH) organise un séminaire Itzykson tous les ans à l’IHES. Il s’agit d’une journée consacrée à un thème de physique mathématique, avec un cours en français et deux ou trois exposés spécialisés en français ou en anglais.Les cartes – surfaces obtenues par recollement de polygones le long de leurs arêtes – intéressent depuis des décennies différents domaines des mathématiques, de l’informatique et de la physique. En particulier, si le recollement est aléatoire, on obtient des cartes aléatoires, qui permettent de décrire des processus stochastiques. Si de plus on décore des cartes aléatoires, on peut décrire des modèles de physique statistique comme le modèle de boucles O(n).Durant cette journée seront présentés divers aspects des cartes, des problèmes de dénombrement aux applications physiques, des idées fondamentales aux développements récents.Un cours et deux exposés auront lieu dans la journée, présentés par : Mireille Bousquet-Mélou, CNRS, LaBRI, Université de BordeauxIgor Kortchemski, CNRS, École polytechnique & ETH ZurichJérémie Bouttier, IMJ-PRG, Sorbonne UniversitéL’inscription est gratuite mais nécessaire et sera possible jusqu’au 13 novembre 2023. Un buffet-déjeuner sera offert aux participants qui s’y seront inscrits. Le séminaire sera filmé et diffusé en différé sur la chaîne YouTube de l’IHES.

French Japanese Conference on Probability & Interactions6-8 March 2024at IHES – Marilyn and James Simons Conference CenterHow to get to IHESThe conference aims at gathering French and Japanese researchers sharing common interests in probability theory related to physical phenomena. Various themes will be considered such as random matrices, stochastic PDEs, particle systems, models in disordered media. Although these domains are represented by different communities, the conference will be the occasion to analyze the connections that occur between those different thematics and to strengthen the collaborations between researchers of both countries.Speakers:Ismael Bailleul, Université de Bretagne OccidentaleQuentin Berger, Sorbonne UniversitéMireille Capitaine, Institut de Mathématiques de ToulouseNicolas Curien, Université Paris-SaclayNizar Demni, Aix-Marseille UniversitéClément Erignoux, Inria Lille Nord-Europe et Université de Lyon 1Masato Hoshino, Osaka UniversityTakashi Imamura (Chiba University)Naotaka Kajino, Kyoto UniversityMylène Maïda, Université de LilleKirone Mallick, CEA, IPhTShuta Nakajima, Meiji UniversityIzumi Okada, Chiba UniversityAkira Sakai, Hokkaido UniversityTomoyuki Shirai, Kyushu UniversityRyokichi Tanaka, Kyoto UniversityMilica Tomasevic, CNRS, École polytechniqueCristina Toninelli, CNRS, Université Paris Dauphine – PSLKenkichi Tsunoda, Kyushu UniversityJulien Vovelle, CNRS, ENS LyonScientific committee:Charles Bordenave (CNRS, Aix-Marseille Université), Benoît Collins (Kyoto University), Arnaud Debussche (ENS Rennes), Takashi Kumagai (Waseda University), Grégory Miermont (ENS Lyon), Tomohiro Sasamoto (Tokyo Institute of Technology).Organizing committee: Anne de Bouard (CNRS, École polytechnique), Thierry Bodineau (CNRS, IHES), Reika Fukuizumi (Waseda University).

An extensive mathematical model for HIV-HCV co-infection is developed. The positivity and boundedness of the model under investigation is established using well-known theorems. The next generation matrix method is used to construct the basic reproduction number for the model. The local and global stabilities of the model are shown using the linearization and Lyapunov function approaches, respectively. Bifurcation analysis and sensitivity analysis of the model are also presented. The findings from the simulations will be presented accordingly.

Séminaire Laurent Schwartz — EDP et applications 

Séminaire Laurent Schwartz — EDP et applications 

Séminaire Laurent Schwartz — EDP et applications 

Séminaire Laurent Schwartz — EDP et applications 

We are interested in a system of particles in singular mean-field interaction and wish to prove that, as the number of particles goes to infinity, two given particles within that system become « more and more » independent, a phenomenon known as propagation of chaos. The interaction we will focus on comes from the Biot-Savart kernel, for which the nonlinear limit of the particle system satisfies the vorticity equation, arising from the 2D incompressible Navier-Stokes system. We build upon a recent work of P.-E. Jabin and Z. Wang to obtain a uniform in time convergence. The approach consists in computing the time evolution of the relative entropy of the joint law of the particle system with respect to the nonlinear limit. We prove time-uniform bounds on the limit, as well as a logarithmic Sobolev inequality. From the latter, the Fisher information appearing in the entropy dissipation yields a control on the relative entropy itself, inducing the time uniformity. This is joint work with A. Guillin and P. Monmarché.

We are going present a multi-scale analysis to derive log-Sobolev inequalities for interacting particle systems. This leads to a generalised Bakry-Emery criterion which can be applied to non-convex potentials. The approach relies on a Hamilton-Jacobi equation know as Polchinski equation. If time allows, we will explain how this multi-scale criterion allows to build Lipschitz transport maps. This talk is based on the survey arXiv:2307.07619 in collaboration with R. Bauerschmidt and B. Dagallier.

In this talk I will present some general strategies for proving (possibly constructive) rate of convergence in the longtime asymptotic for solutions to linear evolution equations. I will next explain how to implement these strategy in the case of the kinetic Fokker-Planck equation for several geometries (torus, whole space with confinement force, bounded domain with reflection condition).

In recent works it has been demonstrated that using an appropriate rescaling, linear kinetic equations with heavy tailed equilibria give rise to a scalar fractional diffusion equation. In this talk an extension of this is presented, where the linear kinetic equations under consideration, not only conserves mass, but also momentum and energy. In the limit, fractional diffusion equations are obtained for the energy and the mass, while the equation for the momentum is trivial. The methods of proof presented rely on spectral analysis combined with energy estimates. It is constructive and provides explicit convergence rates. This is work in progress together with É. Bouin and C. Mouhot.