Combinatorics and Arithmetic for Physics: special days

The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics (renormalisation, combinatorial physics, geometry) or related to its models.

Computation, based on combinatorial structures (graphs,trees, words, automata, semirings, bases) or classic structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation.

Organised by : Gérard H.E. Duchamp, Maxim Kontsevich, Gleb Koshevoy et Hoang Ngoc Minh

Invited speakers :

Nicolas Behr (Université de Paris, IRIF)
Marc Bellon (LPThE-Sorbonne-Univ., Paris and CNRS)
Pierre Cartier (IHES)
Bérénice Delcroix-Oger (Université de Paris, IRIF)
Gérard Duchamp (IHP and LIPN, Univ. Paris XIII)
Thomas Fernique (CNRS and LIPN, Univ. Paris XIII)
Stéphane Gaubert (INRIA and CMAP, École Polytechnique)
Dima Grigoryev (CNRS Painlevé Lab, Univ. Lille)
Dmitry Gurevich (Valenciennes Univ., France)
Richard Kerner (LPTMC, Sorbonne-Univ., Paris)
Maxim Kontsevich (IHES)
Gleb Koshevoy (ISCP, Moscow)
Annie Lemarchand (LPTMC, Sorbonne-Univ., Paris)
Léon Masurel (LPTMC, Sorbonne-Univ., Paris)
Vincel Hoang Ngoc Minh (Univ. Lille and LIPN, Univ. Paris XIII)
Gabriel Morgado (LPTMC, Sorbonne-Univ., Paris)
Frédéric Patras (LJAD, Univ. Côte d’Azur and CNRS)
Karol A. Penson (LPTMC, Sorbonne-Univ., Paris)
Vincent Rivasseau (LPT, Univ. Paris-Sud, Orsay)
Alan Sokal (University College London and New York University)
Pierre Vanhove (IPhT CEA/Saclay, HSE)

      

—————————————– IMPORTANT INFORMATION ——————————————

Due to the evolution of the health situation related to the Coronavirus epidemic, the conference will finally be totally on line. The Zoom link will be sent in the confirmation mail.

———————————————————————————————————————-

Algebraic Structures in Perturbative Quantum Field Theory
A conference in honour of Dirk Kreimer’s 60th birthday

On the occasion of Dirk Kreimer’s birthday, there will be a special issue of SIGMA on « Algebraic Structures in Perturbative Quantum Field Theory ».

Perturbative quantum field theory is essential for precision calculations of observables measured in experiments like the LHC, and therefore it is crucial for our understanding of the physics of the universe. At the same time, it is an extremely rich source of connections to a wide range of active research areas in mathematics. For example, Feynman integrals give rise to interesting motives and periods in algebraic geometry, their renormalization rests on combinatorial Hopf algebras underlying Feynman graphs, and further relations to noncommutative geometry and the moduli space of tropical curves and outer space have also been discovered.

This growing program keeps expanding in both breadth and depth, and exciting young researchers are entering the field. Now is an opportune time to bring together scientists working on all related aspects, to review old and new connections and to advance the state of the art. Lectures by established scientists will be accompanied by talks from young researchers, including a session dedicated to present and discuss open problems.

Close collaborations between mathematicians and physicists have been absolutely key for this kind of research, and many were initiated by Dirk Kreimer. Throughout his career, he made substantial contributions across these topics and led students and collaborators to the profound mathematical structures in perturbative quantum field theory that we are aware of today. Dirk Kreimer spent a particularly productive time at the IHES, and it is an honour that this workshop takes place in its inspiring and interdisciplinary environment.

Organisers: Erik PANZER (University of Oxford) & Karen YEATS (University of Waterloo)

Invited speakers include:

Ali Assem Mahmoud, University of Waterloo
Marc Bellon, LPTHE (Sorbonne Université)
Marko Berghoff, Humboldt-Universität
Spencer Bloch, University of Chicago
Johannes Blümlein, DESY Zeuthen
Michael Borinsky, Nikhef
David Broadhurst, The Open University
Francis Brown, University of Oxford
Yvain Bruned, University of Edinburgh
Alain Connes, IHES & Collège de France
Andrei Davydychev, Moscow State University
Gérald Dunne, University of Connecticut
Kurusch Ebrahimi-Fard, NTNU Trondheim
Loïc Foissy, Université du Littoral Côte d’Opale
Hadleigh Frost, University of Oxford
John Gracey, University of Liverpool
Martin Hairer, Imperial College London
Ralph Kaufmann, Purdue University
Thomas Krajewski, CPT Aix-Marseille
Dominique Manchon, CNRS & Université Clermont-Auvergne
Lukas NABERGALL, University of Waterloo
Sylvie Paycha, Institut für Mathematik Potsdam
Oliver Schnetz, FAU Erlangen-Nürnberg
Christian Schubert, Universidad Michoacana de San Nicolas de Hidalgo
Matt Szczesny, Boston University
Walter van Suijlekom, Radboud Universiteit Nijmegen
Karen Vogtmann, University of Warwick
Raimar Wulkenhaar, Westfälische Wilhelms-Universität Münster

 

Organized with the support of:

Leçons Hadamard
"Nilsequences"
par le Professeur Ben Green

Résumé :

Classical Fourier analysis has found many uses in additive number theory. However, while it is well-adapted to some pro – blems, it is unable to handle others. For example, if one has a set A, and one wishes to know how many 3-term arithmetic progressions are contained in A, then Fourier analysis is useful, but if one wishes to count 4-term progressions then it is not. For this, and other, problems the more general notion of a nilsequence is required. NIlsequences are a kind of «higher order character» forming the basis of what is becoming known as «higher-order Fourier analysis». The talks will be about this theory.

—————————————– IMPORTANT INFORMATION ——————————————

Due to the evolution of the health situation related to the Coronavirus epidemic, the conference will finally be totally on line. The Zoom link will be sent in the confirmation mail.

———————————————————————————————————————-

 

Combinatorics and Arithmetic for Physics: special days

The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics (renormalisation, combinatorial physics, geometry, evolution equations, noncommutative differential equations) or related to its models, but not only.

Computation, based on combinatorial structures (graphs,trees, words, automata, semirings, bases) or classic structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation. »

Organised by : Gérard H.E. Duchamp, Maxim Kontsevich, Gleb Koshevoy et Hoang Ngoc Minh

Updated information (as the Book of Abstracts) can be found there
https://www-lipn.univ-paris13.fr/~duchamp/Conferences/CAP7_2020.html

The concept of topos was introduced by A. Grothendieck during his Séminaire de Géométrie Algébrique du Bois-Marie, which took place at the IHES in the early sixties. The original motivation was that of defining a general notion of space on which one could define cohomological invariants in the algebro-geometric setting needed for proving the Weil's conjectures. In spite of this quite specific technical motivation, the notion of topos appeared at the very beginning as defining a new conception of space, capable of unifying the continuous and the discrete in an harmonious marriage: in the words of Grothendieck "Un lit si vaste en effet (telle une vaste et paisible rivière très profonde…), que “tous les chevaux du roi y pourraient boire ensemble…". "
 
In the following years, new perspectives on the notion on topos emerged. According to Lawvere and Tierney, a topos can be considered not only as a generalized space but as a mathematical universe within which one can carry out most familiar set-theoretic constructions, but which also, thanks to the inherent ‘flexibility' of the notion of topos, can be profitably exploited to construct 'new mathematical worlds' having particular properties. On the other hand, the theory of classifying toposes allows to regard a Grothendieck topos as a suitable kind of first-order theory modulo Morita-equivalence. Toposes have also been proved effective in studying dualities and establishing ‘bridges’ across different mathematical theories with a related semantic content.  
 
The conference aims to illustrate the fruitfulness and wide-ranging impact of the notion of topos, by featuring presentations on new theoretical advances in the subject (including the theory of higher toposes) as well as on applications of toposes in different fields such as number theory, algebraic geometry, logic, functional analysis, topology, mathematical physics and computer science. The conference is preceded by a two-day introductory mini-course for the benefit of students and mathematicians who are not already familiar with topos theory.

Scientific committee : O. CARAMELLO*, P. CARTIER, A. CONNES, S. DUGOWSON, A. KHELIF

23-24 November : Tutorials by: Olivia CARAMELLO and André JOYAL

25-27 November : Invited speakers :

Mathieu ANEL (University Paris-Diderot)
Luca BARBIERI-VIALE (Università degli Studi di Milano)
Jean BÉNABOU (University Paris 13)
Caterina CONSANI (Johns Hopkins University, Baltimore)
Thierry COQUAND (University of Göteborg)
Simon HENRY (Radboud University, Nijmegen)
André JOYAL (Université du Quebec, Montréal)
Mike PREST (University of Manchester)
Urs SCHREIBER (Eduard Čech Institute for Algebra, Geometry and Physics, Prague)
Carlos SIMPSON (University of Nice-Sophia-Antipolis) 
Michel VAQUIÉ (University Paul Sabatier, Toulouse)

25 & 27 November: Short Communications Speakers

Ingo BLECHSCHMIDT (University of Augsburg)
Matias DATA (Universidad de Buenos Aires)
Jonas FREY (Copenhagen University)
Camell KACHOUR
Guilherme Frederico LIMA de CARVALHO e SILVA (University of Cambridge)
Pietro POLESELLO (Universita di Padova)
David ROBERTS (University of Adelaide)
Anna Carla RUSSO (University of Salerno & Université Paris-Diderot)
Alex SIMPSON (University of Ljubljana)
Zoran  SKODA (University of Hradec Kralové)
Christopher TOWNSEND (Royal Bank of Canada)

* holder of a fellowship "L'Oréal-Unesco for Women in Science" which supports the conference
 

The non-official website of the conference  ­(maintained by S. Dugowson)
contains further materials provided by the speakers
­in connection with their talks and edited versions of the videos of the tutorials.

List of speakers includes:

      Thomas ALAZARD (ENS Paris)
      Valeria BANICA (Université d'Evry Val d'Essonne)
      Diego CORDOBA (ICMAT)
      Mihalis DAFERMOS (University of Cambridge)
      Camillo DE LELLIS (Universität Zürich)
      Benjamin DODSON (Johns Hopkins University)
      Patrick GERARD (Université Paris-Sud)
      Pierre GERMAIN (Courant Institute of Mathematics)
      Cécile HUNEAU (ENS Paris)
      Alexandre IONESCU (Princeton University)
      Robert JERRARD (University of Toronto)
      Thomas KAPPELER (Universität Zürich)
      Rowan KILLIP (UC Los Angeles)
      Michal KOWALCZYK (Universidad de Chile)
      David LANNES (Université de Bordeaux 1)
      Andrew LAWRIE (University of California, Berkeley)
      Enno LENZMANN (Universität Basel)
      Andrea NAHMOD (University of Massachusetts, Amherst)
      Fabio PUSATERI (Princeton University)
      Benjamin SCHLEIN (Universität Zürich)
      Christopher SOGGE (Johns Hopkins University)
      Vlad VICOL (Princeton University)
      Hatem ZAAG (Université Paris 13)

Organising Committee:

      Thomas DUYCKAERTS (Université Paris 13)
      Frank MERLE (Université de Cergy-Pontoise & IHÉS)
      Jérémie SZEFTEL (Université Pierre et Marie Curie)

Crédit photographique: © CNRS Photothèque
RAJAU Benoît (UMR7538 – Laboratoire de physique des lasers (LPL), VILLETANEUSE et VRIGNAUD François (UMR6172 – XLIM – LIMOGES)

With the support of

 

SÉMINAIRE GROTHENDIECK

Organisé par : L. Barbieri-Viale, F. Brown, D. Gaitsgory et L. Lafforgue 

Conférenciers :

Yves André (Institut de mathématiques de Jussieu)
Joseph Ayoub (Universität Zürich)
Michael Hopkins (Harvard University)
Moritz Kerz (Universität Regensburg) 

Exposé extra-mathématique :

Céline Pessis (coordinatrice du livre "Survivre et vivre. Critique de la science, naissance de l'écologie")

Présentation et projection d’un film :

"L'espace d'un homme" par  Hervé Nisic

 

 

David Ruelle a apporté nombre de contributions majeures et durables dans plusieurs domaines de la physique : théorie quantique des champs axiomatique (théorie de Haag-Ruelle) ; mécanique statistique de l’équilibre (équations de Dobrushin-Lanford-Ruelle) ; théorie de la turbulence (concept d’ « attracteur étrange » de Ruelle-Takens) ; théorie des systèmes dynamiques et du chaos (opérateurs de transfert, mesures SRB (Sinaï, Ruelle, Bowen)) ; mécanique statistique du non-équilibre. Il est devenu professeur permanent à l’IHÉS en 1964 (professeur honoraire depuis 2000).

Organisé par : Thibault Damour et Jean-Pierre Eckmann

Conférenciers :

15h00-16h00
Viviane BALADI (CNRS-IMJ-PRG) 
Spectres d'opérateurs de transfert et billards de Sinai

Depuis une douzaine d'années, on sait contrôler le spectre d'un opérateur de transfert agissant sur un espace de distributions anisotropes. Ceci a permis de simplifier les preuves de résultats obtenus par d'autre méthodes (partitions de Markov, tours de Lai-Sang Young), mais aussi d'obtenir de nouveaux résultats qui avaient résisté aux autres approches.

Avec Mark Demers et Carlangelo Liverani nous avons ainsi récemment montré que les flots billards de Sinai mélangent exponentiellement vite. L'exposition de ce résultat sera ainsi l'occasion de donner un rapide panorama du sujet.

16h30-17h30
Hans Henrik RUGH (Université Paris-Sud Orsay)
The Milnor-Thurston determinant and the Ruelle transfer operator

The topological entropy htop of a continuous piecewise monotone interval map measures the exponential growth in the number of monotonicity intervals for iterates of the map. Milnor and Thurston showed that exp(-htop) is the smallest zero of an analytic function, now coined the Milnor-Thurston determinant, that keeps track of relative positions of forward orbits of critical points. On the other hand exp(htop) equals the spectral radius of a Ruelle transfer operator L, associated with the map. Iterates of L keep track of inverse orbits of the map. For no obvious reason, a Fredholm determinant for the transfer operator has not only the same leading zero as the M-T determinant but all peripheral (those lying in the unit disk) zeros are the same.

In the talk I will show that on a suitable function space, the dual of the Ruelle transfer operator has a regularized determinant, identical to the Milnor-Thurston determinant, hereby providing a natural explanation for the above puzzle.

17h45 : Reception

 

The aim of this workshop is to bring together mathematicians and computer scientists around some talks on recent results from statistics, machine learning and more generally data science research. Various topics in machine learning, optimization, deep learning, optimal transport, inverse problems, statistics and problems of scientific reproducibility will be presented.

Registration is free and open to January 20, 2020.

Organised by: Alexandre Gramfort (INRIA) and Thanh Mai Pham NGOC (LMO Orsay)

Invited speakers:

Sarah Cohen-Boulakia (LRI, Paris-Sud)
Victor-Emmanuel Brunel (ENSAE/CREST)
Steve Oudot (INRIA)
Charles Soussen (CentraleSupélec)
Gilles Blanchard (IHES)
Quentin Merigot (Paris-Sud)

The second joint workshop between Nokia Bell Labs and the Institut des Hautes Études Scientifiques will take place on the next November 25.

To celebrate this event, we will have four excellent conferences given by experts in their field:

Stéphane Mallat (Collège de France) will adress Multiscale Models for Image Classification and Physics with Deep Networks ;

Jakob Hoydis (Nokia Bell Labs France/Paris-Saclay) will explain Recent Progress in End-to-End Learning for the Physical Layer ; 

Michael Douglas (Simons Center in Geometry and Physics – SUNY) will think about How will we do mathematics in 2030? ;

Philippe Jacquet (Inria – Nokia Bell Labs) will compare AI vs Information theory and learnability.

This second joint workshop marks Nokia Bell Labs donation to the Institut des Hautes Études Scientifiques in 2017. Nokia Bell Labs is one of the largest and oldest private research laboratories in the world and perhaps the only one to offer a continuous flow of impressive scientific discoveries and theoretical contributions over the past century.

Organisers: Philippe JACQUET (Nokia – FR/Paris-Saclay), Emmanuel ULLMO (IHES)

The Ising model is one of the most classical models of statistical physics and has been a testing ground for mathematicians and physicists for a century. On the occasion of its 100th anniversary, postponed from 2020 to 2022, the Institut des Hautes Études Scientifiques (IHES) organises a special conference that will take place 30 May to 3 June 2022, with talks from various fields involved in the study of the model.

This event should serve as a platform between mathematicians and physicists working in the domain. 

This conference is organised by: Hugo Duminil-Copin (IHES), Slava Rychkov (IHES) and Béatrice de Tilière (Cérémade, Univ. Paris-Dauphine)

 

© Clément Hongler (EPFL)

 

List of speakers and round-table participants:

Michael AIZENMAN, Princeton University (Speaker)
Roland BAUERSCHMIDT, University of Cambridge (Speaker)
Edouard BRÉZIN, ENS Paris (Round-table)
Michele CASELLE, Università di Torino (Speaker)
Loren COQUILLE, Université Grenoble-Alpes (Speaker)
Victor DOTSENKO, LPTMC Jussieu (Speaker)
Daniel FISHER, Stanford University (Speaker)
Jürg FRÖHLICH, ETH Zürich (Round-table)
Alessandro GIULIANI, Università di Roma 3 (Speaker)
Rafael GREENBLATT, Universita’ degli Studi Roma Tre (Speaker)
Geoffrey GRIMMETT, University of Cambridge (Round-table)
Clément HONGLER, EPFL (Speaker)
Arthur JAFFE, Harvard University (Round-table)
Rick KENYON, Yale University (Speaker)
Joel LEBOWITZ, Rutgers University (Round-table)
Eyal LUBETZKY, Courant Institute, NYU (Speaker)
Giuseppe MUSSARDO, SISSA Trieste (Speaker)
Eveliina PELTOLA, HCM University of Bonn (Speaker)
Ara SEDRAKYAN, Yerevan Physics Institute (Speaker)
Stanislav SMIRNOV, University of Geneva (Speaker)
Tom SPENCER, IAS (Round-table)
Vincent TASSION, ETH Zürich (Speaker)
Fabio TONINELLI, Technical University of Vienna (Speaker)
Yvan VELENIK, Université de Genève (Speaker)
Alessandro VICHI, Università di Pisa (Speaker)
Wendelin WERNER, ETH Zürich (Speaker)
Jean ZINN-JUSTIN, CEA Saclay (Speaker)

"Quantum Gravity: Physics and Philosophy"
ERC Project Philosophy of Canonical Quantum Gravity

 

List of speakers includes:

Costas BACHAS (Department of Physics, Ecole Normale Supérieure)
Michel BITBOL (Archives Husserl, CNRS)
Steven CARLIP (Department of Physics, University of California Davis)
Alain CONNES (IHES)
Erik CURIEL (Munich Center for Mathematical Philosophy)
Dennis DIEKS (University of Utrecht)
Yuval DOLEV (Department of Philosophy, Bar-Ilan University)
Sebastian de HARO (University of Amsterdam)
Gary HOROWITZ (Department of Physics, University of California Santa Barbara)
Theodore JACOBSON (Department of Physics, University of Maryland)
Claus KIEFER (Institut of Theoretical Physics, University of Cologne)
Carlo ROVELLI (Center of Theoretical Physics, Luminy)
Gabriele VENEZIANO (Theoretical Physics Department, CERN)
Tiziana VISTARINI (Department of Philosophy, University of Colorado Boulder)

 

Organising Committee:

Gabriel CATREN (CNRS, Laboratoire SPHERE)
Thibault DAMOUR (IHES)
Elie DURING (Université Paris Nanterre, Laboratoire IRePh)
Federico ZALAMEA (CNRS, Laboratoire SPHERE)