Higher categorical symmetries have received widespread attention in recent years, generalising in various ways the usual notion of symmetry. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging ordinary symmetries. Specialising to certain finite group generalisations of the (2+1)d transverse-field Ising model, I will explain what it means for a quantum lattice model to have such a symmetry structure.  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_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

À l’occasion du centenaire de la naissance de René Thom, l’IHES organise trois jours de conférence les 20, 21 et 22 septembre 2023. Conférenciers invités : Norbert A’Campo, Univ. De BâleDaniel Bennequin, Institut Mathématique de Jussieu (IMJ-PRG)Alain Chenciner, IMCCE/Observatoire de Paris Antoine Danchin, Institut Pasteur                     Ivar Ekeland, Université Paris-DauphineSara Franceschelli, ENS LyonEmmanuel Giroux, CNRS et ENSMikhail Gromov, IHESKrzysztof Kurdyka, Université Savoie Mont BlancCherif Matta, Mount Saint Vincent University, Halifax, CanadaJean Petitot, EHESSOscar Randal-Williams, Université de CambridgeAna Rechtman, Université Grenoble-AlpesDennis Sullivan, City University of New York, Graduate Center                       Bernard Teissier, IMJ-PRGWolfgang Wildgen, Université de BrêmeComité scientifique : Marie-Claude Arnaud, IMJ-PRG, Marc Chaperon, IMJ-PRG, coordinateur, Antoine Danchin, Institut Pasteur, Yakov Eliashberg, Stanford University, Maxim Kontsevich, IHES, Cédric Villani, Université Lyon I & IHESComité d’organisation : Jean-Pierre Bourguignon, IHESRené Thom (1923-2002)Professeur permanent à l’IHES de 1963 à 1990René Thom a couvert un champ scientifique immense : d’abord en ouvrant des champs nouveaux en topologie, cette branche des mathématiques qui s’intéresse aux formes à déformation près, et dans l’étude de la dynamique. Il a ensuite créé une « mathématique de la morphogenèse », proposant des modèles pour la biologie et aussi pour les sciences humaines.Ces proposi­tions, souvent regroupées sous le nom de « théorie des catastrophes », ont quelque fois été controversées. René Thom a consacré la suite de sa vie scientifique à l’étude de la biologie théorique et surtout à la philosophie aristotélicienne.

The scope of this in-person week-long meeting that will take place at the Institut des Hautes Études Scientifiques (IHES) in Bures-sur-Yvette, is to bring together scientists from the LSC Committee with invited experts and the IHES scientists to present the latest progress in understanding evolution as a process of learning, and conversely, evolution of learning, in the context of their respective disciplines, to fuel discussion of the challenges and brainstorm on synergistic solutions.INVITED SPEAKERS:INVITED SENIOR GUESTS:INVITED JUNIOR GUESTS:More details in the Profiles section. ORGANIZERS:Yves Barral, ETH ZurichEugene Koonin, NIHMikhail Gromov, IHES & NYUBob Penner, IHES & UCLASCIENTIFIC COMMITTEE:Yann LeCun, NYU & Meta AINicolas Minc, U. Paris Cité/CNRSPierre-Yves Oudeyer, INRIA BordeauxYukiko Yamashita, MITEXECUTIVE ORGANIZATION: Grazia Gonella, ETH ZurichCONTACT: lsc@biol.ethz.ch

Most people are familiar with periodic tessellations and lattices; from the patio floor at the reception building to their favourite spin systems. In this talk, I will discuss two less familiar families of tessellations and their possible connections to high energy physics, condensed matter physics, and mathematics: hyperbolic tessellations and quasicrystals. After introducing the basics of regular hyperbolic lattices, I will survey constructions and surprising properties of quasicrystals (like the Penrose tiling), including their classically forbidden symmetries, long-range order, and self-similar structure. Inspired by the AdS/CFT correspondence, I will describe a mathematical relationship between hyperbolic lattices in (D+1)-dimensions and quasicrystals in D-dimensions, as well as the resolution of a conjecture by Bill Thurston. Based on work to appear with Latham Boyle. 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_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

I will explain recent new results about the category of localizing motives — the target of the universal localizing invariant of stable k-linear infinity-categories (over some base k), commuting with filtered colimits. In particular, I will explain the most striking property of this category: it is rigid as a large symmetric monoidal category (in the sense of Gaitsgory and Rozenblyum). I will also explain how to compute morphisms in this category, obtaining an effective description of the algebraic version of K-homology and more generaly of Kasparov’s KK-theory. As a special case, we will deduce the corepresentability of TR (by the reduced motive of the affine line) and of the topological cyclic homology (by the unit object of the kernel of A1-localization), when restricted to the motives of connective E1-rings. Another special case is the comparison theorem of two approaches to K-theory of formal schemes: the classical continuous K-theory is equivalent to the K-theory of the category of nuclear modules, which was defined by Clausen and Scholze. If time permits, I will explain an application to the p-adic analogue of the lattice conjecture. Namely, we construct a symmetric monoidal functor from smooth and proper dg categories over Cp to perfect modules over the p-completion of KU, with a natural map from the K(1)-local K-theory (this map is conjecturally an equivalence, but this seems to be out of reach).  ========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.

“Wall-Crossing Structures, Analyticity, and Resurgence”,  a mini-school organized by Maxim Kontsevich and Yan Soibelman This conference is organized by Maxim Kontsevich (IHES), and Yan Soibelman (Kansas State University).The main emphasis will be on the new approach to resurgent series via analytic wall-crossing structures (an alternative to the traditional alien calculus), as well as the detailed study of examples coming from quantum Chern-Simons theory, WKB expansions and, more generally, holomorphic Floer theory.The program includes 3 mini-courses, given by:Jørgen E. Andersen (SDU)Maxim Kontsevich (IHES)Yan Soibelman (Kansas State University)and research presentations, given by:Philip Boalch (IMJ-PRG)Pierrick Bousseau (University of Georgia)Veronica Fantini (IHES)Segei Gukov (Caltech)Lotte Hollands (Heriot Watt University)Kohei Iwaki (The University of Tokyo)Marcos Mariño (University of Geneva)William Mistegård (SDU)David Sauzin (Observatoire de Paris-Meudon)Campbell Wheeler (MPI Bonn)

The year 2023 marks the centenary of the birth of Louis Michel, the first Professor of Theoretical Physics at IHES. On this occasion, Thibault Damour and Slava Rychkov organize a one-day commemoration on May 15, 2023, at IHES. Several presentations will be given by lecturers linked to Louis Michel or to his work:Jean-Pierre Bourguignon, CNRS-IHESHenri Epstein, CNRS-IHESDenis Gratias, CNRS-Institut de Recherche de Chimie ParisDavid Ruelle, IHESSlava Rychkov, IHESMarjorie Senechal, Smith CollegeBoris Zhilinskii, Univ. du Littoral Côte d’OpaleOrganizers: Thibault DAMOUR (IHES) and Slava Rychkov (IHES).

Séminaire Laurent Schwartz — EDP et applications 

Séminaire Laurent Schwartz — EDP et applications 

This will be a discussion about large language models such as OpenAI’s GPT series, oriented towards physicists and mathematicians. After a brief survey of the state of the art, we describe transformer models in detail, and discuss current ideas on how they work and how models trained to predict the next word in a text are able to perform other tasks displaying intelligence.  ========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.

  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_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

I’ll explain how the quantization of Hitchin integrable system can be formulated in the N=2 supersymmetric gauge theory with the help of half-BPS surface defects. I’ll first review the universal oper for the Gaudin model constructed from a current algebra, and relate it to the constraints for the coinvariants of the affine Kac-Moody algebra with the twisted vacuum module. In the N=2 gauge theory side, we consider two types of surface defects, the « canonical » surface defect and the « regular monodromy » surface defect, inserted on top of each other. The correlation function of the surface defects is shown to give a basis of coinvariants with the twisted vacuum module. The insertion of twisted vacuum module is known to give the action of Hecke modification on the coinvariants. I’ll define the Hecke operator as an integral of the image of Hecke modifications, which is shown to factorize due to the cluster decomposition of the two surface defects. The factorization explains why the action of the Hecke operator is diagonal. Using this factorization property and the relation with the universal oper, I show the sections of the Hecke eigensheaf give common eigenfunctions of the quantum Hitchin Hamiltonians (with the eigenvalues parametrizing the space of opers), explaining the statement of Beilinson and Drinfeld in the N=2 gauge theory framework. ========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.