Arithmetic Algebraic GeometryJan Nekovář was a mathematician who worked and has made many significant and seminal contributions to algebraic geometry. He left us prematurely in November 2022. Here is a tribute note (in French) by Pierre Colmez.In his memory, Anna Cadoret, IMJ-PRG, Wiesława Nizioł, IMJ-PRG, and Sarah Zerbes, ETH Zürich, organize a conference in arithmetic algebraic geometry at IHES from October 9th to 13th, 2023.This is an international conference in arithmetic geometry, aimed at covering some of the most recent advances in the field with a focus on the areas Jan Nekovář was interested in. Invited Speakers:Tomoyuki Abe, IPMU – University of Tokyo  Spencer Bloch, University of Chicago  Ana Caraiani, Imperial College London – University of BonnHenri  Darmon, McGill University  Vesselin Dimitrov, Institute for Advanced Studies  Matthew  Emerton, University of Chicago  Veronika  Ertl, Universitat Regensburg  Hélène Esnault, Frei Universität Berlin  Olivier Fouquet, Université de Franche-Comté Alexander Goncharov, Yale University  Giada Grossi, CNRS, Université Sorbonne Paris Nord      Jie Lin, Universität Duisburg-Essen  David  Loeffler, University of Warwick   Akhil Mathew, University of Chicago   James Newton, University of Oxford  Alexander Petrov, Harvard University  Alena Pirutka, New York University  Tony Scholl, University of Cambridge   Yunqing Tang, University of California – Berkeley  Jacob Tsimerman, University of Toronto    IHES thanks all the donors of the 2021 Friends of IHES Gala for making this conference possible.

We propose using smeared boundary states as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches in CFTs and of the entanglement spectrum in massive theories. It gives a simple criterion for choosing which boundary state should correspond to which combination of bulk operators, and leads to a rudimentary phase diagram of the theory in the vicinity of the RG fixed point corresponding to the CFT, as well as rigorous upper bounds on the universal amplitude of the free energy. In the case of the 2d minimal models explicit formulae are available. As a side result we show that the matrix elements of bulk operators between smeared Ishibashi states are simply given by the fusion rules of the CFT. 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 why positive representations of fundamental groups of surfaces satisfy a « collar lemma » similar to the classical collar lemma for hyperbolic geometry, and have associated positive cross-ratios. As a consequence, I will deduce that positive representations form closed subsets of the representation variety. I will spend some time recalling what a positive representation is, what the associated cross-ratios are, and explain the main new object that we shall use and that we call « photons ». This is joint work with Jonas Beyrer, Olivier Guichard, Beatrice Pozzetti and Anna Wienhard.

Quantum representations are families of finite-dimensional representations of mapping class groups satisfying strong compatibility conditions. One of the most well-known (the so-called SO(3)-TQFT) depends on a parameter q which is a root of unity of order 2r (r odd). These representations preserve a Hermitian form: recently, with B. Deroin, we explained how to compute its signature (among other things). More recently, I observed that this computation is related to the trace field of the 2-bridge knot K(r,s) where q=exp(iπs/r). During the talk, I will explain this relation and the objects involved in it.

Assume certain comparison between non-commutative Hodge structures and classical Hodge structures, we show the categorical enumerative invariants associated with a smooth projective family of Calabi-Yau 3-folds satisfy the holomorphic anomaly equations. This naturally leads to the study of geometric structures on moduli spaces of smooth projective Calabi-Yau 3-folds. ========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.

For certain problems, taking the Borel sum of an intuitively chosen divergent series solution will often produce a holomorphic solution. When does this happen, and what is special about the holomorphic solutions obtained in this way? We will present work in progress on these questions, focusing on two kinds of problems: linear ODEs and integrals over Lefschetz thimbles.Day IIThe second day’s lectures are dedicated to a family of examples: the Airy-Lucas functions introduced by Charbonnier et al. (arXiv:2203.16523). These functions satisfy linear ODEs that generalize the Airy equation. They can also, like the Airy function, be expressed as thimble integrals. We will explain, from both perspectives, why these solutions can be obtained by Borel summation.We will conclude by describing general classes of linear ODEs and 1d thimble integrals that can be analyzed in the same way. ========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.

For certain problems, taking the Borel sum of an intuitively chosen divergent series solution will often produce a holomorphic solution. When does this happen, and what is special about the holomorphic solutions obtained in this way? We will present work in progress on these questions, focusing on two kinds of problems: linear ODEs and integrals over Lefschetz thimbles.Day IWe will start the first day’s lectures with a presentation of our questions and an overview of our expected results.Next, we will review the Laplace and Borel transforms from a new perspective that highlights the geometric structure of the Borel plane. This geometric structure is relevant to both of the kinds of problems we study. For linear ODEs, the solutions that can be obtained by Borel summation are indexed by singular points on the Borel plane. Similarly, integrals over Lefschetz thimbles can be recast as Laplace integrals along rays departing from singular points. ========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.

ANNULÉ ET REPORTÉIn this talk we will revisit the bootstrap hypothesis in the two-dimensional case from a mathematical perspective. The bootstrap equations is a consistency for the CFT four-point correlation functions. Therefore, the following question is not mathematically clear: (Math Question) If the four-point correlation functions satisfy the bootstrap equations, can we define a multi-point correlation functions? (Is it convergent and consistent?) After introducing the notion of a full vertex algebra, which is equivalent to the fact that the four-point correlation functions satisfy the bootstrap equations, we will explain that all n-point correlation functions converge and are consistent when the full vertex algebra satisfies certain finiteness. An crucial step in the proof is to show that the operad of configuration spaces acts on representations of the full vertex algebra (under the finiteness assumption). We will explain this idea in detail. 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.

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.