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.

Discrete subgroups of semisimple Lie groups arise in a variety of contexts, sometimes « in nature » as monodromy groups of families of algebraic manifolds, and other times in relation to geometric structures and associated dynamical systems. I will explain a method to establish that monodromy groups of certain variations of Hodge structure give Anosov representations, thus relating algebraic and dynamical situations. Among many consequences of these interactions, I will explain some uniformization results for domains of discontinuity of the associated discrete groups, Torelli theorems for certain families of Calabi-Yau manifolds (including the mirror quintic), and also a proof of a conjecture of Eskin, Kontsevich, Möller, and Zorich on Lyapunov exponents. The discrete groups of interest live inside the real linear symplectic group, and the domains of discontinuity are inside Lagrangian Grassmanians and other associated flag manifolds. The necessary context and background will be explained.

The horocycle flow on hyperbolic surfaces has attracted considerable attention in the last century. In the ’30s, Hedlund proved that all horocycle orbits are dense in closed hyperbolic surfaces, and the classification problem for horocycle orbit closures has been solved for geometrically finite surfaces. We are interested in the topology and dynamics of horocycle orbits in the geometrically infinite setting, where our understanding is much more limited.In this talk, I will discuss joint work with Or Landesberg and Yair Minsky: we give the first complete classification of orbit closures for a class of Z-covers of closed surfaces. Our analysis is rooted in a seemingly unrelated geometric optimization problem: finding a best Lipschitz map to the circle. We then relate the topology of horocycle orbit closures with the dynamics of the minimizing lamination of maximal stretch, as studied by Guéritaud-Kassel and Daskalopoulos-Uhlenbeck.

 Transposable elements (TEs), one type of mobile genetic elements, often represent a large part of eukaryotic genomes and were long regarded only as selfish genomic parasites. We are now coming to understanding of the complex relationships between TEs and their host organisms — not only in the germline but in the soma too.The repetitive nature of TE has prevented to fully grasp the level of their activity with molecular biology and sequencing techniques so far. This is particularly true of somatic transposition in the healthy tissues on the whole-genome scale, as these events represent rare variants difficult to accurately detect with bulk short-read sequencing approaches.I will give a brief overview of the field and present our ongoing study of transposable elements mobility in D. melanogaster with long-read sequencing techniques. We were able to identify an endogenous LTR retroelement rover that is somatically active in the healthy gut tissues by tracing back sequence variants of the inserted sequences to the fixed rover copies. We dissected the transcriptional landscape as well as the local sequence and chromatin environment of the fixed copies and hypothesize that its activity may be determined by the upstream locus-specific chromatin features.

Probability and analysis informal seminarIn this talk, we will consider a classical model of random interfaces known as the grad phi (or Ginzburg-Landau) model. The model first received rigorous consideration in the work of Brascamp-Lieb-Lebowitz in 1975. Since then, it has been extensively studied by the mathematical community and various aspects of the model have been investigated regarding for instance the localization and delocalization of the interface, the hydrodynamical limit, the scaling limit, large deviations etc.  Most of these results were originally established under the assumption that the potential encoding the definition of the model is uniformly convex, and it has been an active line of research to extend these results beyond the assumption of uniform convexity. In this talk, we will introduce the model, some of its main properties, and discuss a result of localization and delocalization for a class of convex (but not uniformly convex) potentials. ========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.