14e séminaire ITZYKSON : Dualité markovienne : méthodes algébriques et applications

Le 14e séminaire Itzykson est organisé par Jean-René Chazottes (CPHT), Guillaume Dubach (CMLS), Ruben Minasian (IPhT) et Julio Parra-Martinez (IHES). 
Depuis bientôt une quinzaine d’années l’axe math-physique de la 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 et deux ou trois exposés spécialisés (en français ou en anglais selon le choix des orateurs).
Le prochain séminaire Itzykson portera sur la dualité markovienne, et ses liens avec les algèbres de Lie et les systèmes de particules en interaction. Ces sujets sont reliés par une même idée directrice : l’approche algébrique de la dualité, qui permet de construire et d’analyser des processus markoviens exactement solubles. Le séminaire donnera des perspectives algébriques, probabilistes et physiques sur des résultats récents, notamment au sujet des symétries des générateurs markoviens, des interprétations trajectorielles en génétique des populations, et des fluctuations macroscopiques hors d’équilibre.
Les cours et exposés de cette journée seront présentés par : 

Cristian Giardinà (Università di Modena e Reggio Emilia)

Noemi Kurt (Goethe-Universität Frankfurt)

Frank Redig (TU Delft)

L’inscription est gratuite mais nécessaire et sera possible jusqu’au 23 novembre 2026. 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.

Combinatorics and Arithmetic for PhysicsThe meeting’s focus is about 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 (commutative and noncommutative) or related to their models. Computations, based on combinatorial structures (graphs,trees, words, automata, semirings, bases) or classical structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implementation and experimentation.
Organized by: Gérard H. E. DUCHAMP, Maxim KONTSEVICH, Gleb KOSHEVOY and Karol A. PENSON.
Speakers:

Ariana Chin (UCLA)
Lucia Di Vizio (Université de Versailles-St Quentin)
Florian Fürnsinn (Universität Wien)
Stéphane Gaubert (INRIA)
Gleb Koshevoy (IITP, Moscow)
Toshiki Nakashima (Sophia University, Tokyo)
Robert Penner (University of California & IHES)
Darya Polyakova (Hamburg University)
Volodya Roubtsov (Université d’Angers)
Theo Saporiti (Université Paris-Saclay)
Travis Scrimshaw (Hokkaido University)
Mahsa Shirmohammadi (IRIF, Université de Paris)
 

Sponsors: IHES – Math-STIC – LIPN (UMR-7030) – LPTMC (Univ-Paris 6) –   INRIA – GDR EFI –  Université Sorbonne Paris Nord
Scientific Committee:Joseph Ben Geloun (LIPN-Paris XIII), Alin Bostan (INRIA), Marek Bożejko (Wroclaw University), Vincent Rivasseau (Orsay-CEA), Pierre Simonnet (Univ. Corse)

 
 

This course has two parts. In the first we will define a general notion of integer point in a higher Teichmüller space and two invariants thereof, the arithmetic dimension and the arithmetic height. The aim is to show finiteness, modulo the mapping class group action, of the number of integer points for which both invariants are bounded.
In the second part we will give the main steps leading to the recent result of Frączyk, Hurtado and Raimbault, stating that the topological complexity of an arithmetic locally symmetric space is bounded by its volume.
Both parts rely on the arithmetic Margulis lemma proven by the same authors as a consequence of Breuillard’s height gap theorem.

This course has two parts. In the first we will define a general notion of integer point in a higher Teichmüller space and two invariants thereof, the arithmetic dimension and the arithmetic height. The aim is to show finiteness, modulo the mapping class group action, of the number of integer points for which both invariants are bounded.
In the second part we will give the main steps leading to the recent result of Frączyk, Hurtado and Raimbault, stating that the topological complexity of an arithmetic locally symmetric space is bounded by its volume.
Both parts rely on the arithmetic Margulis lemma proven by the same authors as a consequence of Breuillard’s height gap theorem.

This course has two parts. In the first we will define a general notion of integer point in a higher Teichmüller space and two invariants thereof, the arithmetic dimension and the arithmetic height. The aim is to show finiteness, modulo the mapping class group action, of the number of integer points for which both invariants are bounded.
In the second part we will give the main steps leading to the recent result of Frączyk, Hurtado and Raimbault, stating that the topological complexity of an arithmetic locally symmetric space is bounded by its volume.
Both parts rely on the arithmetic Margulis lemma proven by the same authors as a consequence of Breuillard’s height gap theorem.

This course has two parts. In the first we will define a general notion of integer point in a higher Teichmüller space and two invariants thereof, the arithmetic dimension and the arithmetic height. The aim is to show finiteness, modulo the mapping class group action, of the number of integer points for which both invariants are bounded.
In the second part we will give the main steps leading to the recent result of Frączyk, Hurtado and Raimbault, stating that the topological complexity of an arithmetic locally symmetric space is bounded by its volume.
Both parts rely on the arithmetic Margulis lemma proven by the same authors as a consequence of Breuillard’s height gap theorem.

Seed Seminar of Mathematics and Physics
AI and the Future of Mathematics and Physics 
The Jacobian conjecture states that for any polynomial map from  to itself, if it is everywhere a local diffeomorphism, then it admits a polynomial global inverse. In this talk, I will present the three-dimensional counterexample to this conjecture posted by L. Alpöge on  and credited to Claude. 
After stating the conjecture and the counterexample, I will explain the geometric interpretation of the counterexample which was posted by A. Jiang and credited to ChatGPT. Finally I will give some observations about the history of the conjecture and its significance.
We answer this problem coming from representation theory using topological tools. On the representation theory side we define extensions of Habiro type rings. On the topological side, we construct a universal Jones link invariant and a universal Alexander link invariant. Putting these together, our universal invariants of geometrical nature take values in the extended Habiro rings that we construct.
More information: https://seedseminar.pages.math.cnrs.fr/program/#november-4-2026
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Seed Seminar of Mathematics and PhysicsAI and the Future of Mathematics and Physics
We will start with a brief technical overview of Large Language Models and then discuss their impact on the theoretical sciences. We will summarize the results of a recent study “TheoPhysEval” https://arxiv.org/abs/2610.16733 where we evaluated AI agents on unsolved physics problems. The talk is aimed at initiating a broader discussion on how physics pedagogy and research must evolve in light of recent technological advances.
The zoom link is available by subscribing to the mailing list: sympa@listes.math.cnrs.fr
More information: https://seedseminar.pages.math.cnrs.fr/program/#november-4-2026
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Séminaire d’Analyse
Scattering theory describes the large-time behavior of nonlinear evolution equations through comparison with a linear flow. This raises a further question: can the nonlinear correction to the asymptotic state be smoother than the initial data?I will begin with an introduction to scattering for nonlinear Schrödinger equations, highlighting several developments that motivate this question. I will then present a deterministic smoothing result for the two-dimensional cubic equation. Assuming that a solution scatters in the harmonic Sobolev space $(mathcal H^s)$, with $(s>0)$, the difference between its scattering state and its initial datum belongs to $(mathcal H^{s+sigma})$ for every $(0<sigma<min{2s,1})$. The proof combines the lens transform, which turns the large-time problem into a finite-time endpoint problem, with bilinear Strichartz estimates and harmonic spectral analysis. The emphasis will be on the mechanism behind the regularity gain.
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I will discuss some recent progress on harmonic maps from surfaces to spheres which are energy minimizing representatives of orthogonal representations. What can be said about their shapes and their limit geometry as the dimension of the representations grows to infinity? This is partly joint with Riccardo Caniato and Xingzhe Li.

 Chatterji and Venkataramana, motivated by Nori’s problem, asked for a real algebraic semisimple Lie group G and a simple Lie subgroup H of G, whether a Zariski-dense discrete subgroup of G, intersecting H in a lattice, is itself a lattice in G. After discussing what is known related to this question and Nori’s problem, we will address a similar version of this question for the k-points of semisimple groups defined over a non-Archimedean local field k, and provide examples for which a positive answer fails. This is based on a combination theorem for discrete subgroups of matrix groups over discretely valued fields. We will also discuss a construction of non-Fuchsian hyperbolic groups that quasi-isometrically embed as subgroups of matrix groups over a discretely valued field. 

Séminaire de géométrie arithmétique
Jacobi’s theta function $Theta(q) := 1 + 2q + 2q^4 + 2q^9 + cdots $, and more generally the theta functions associated to positive-definite quadratic forms, have the property that they are modular forms of half-integral weight. The usual proof of this fact is completely analytic in nature, using the Poisson summation formula. However, $Theta$ is also related to diffusion of heat on a uniform circle-shaped material: it is a restriction of the fundamental solution to the heat equation on a circle. By algebraically characterizing the heat equation as a specific flat connection on a certain bundle on a modular curve, we produce a completely algebraic technique for proving modularity of theta functions. More specifically, we produce a refinement of the algebraic theory of theta functions due to Moret-Bailly, Faltings–Chai, and Candelori. As a consequence of the algebraic nature of our theory and the fact that it applies to indefinite quadratic forms / non-ample line bundles (which the prior algebraic theory does not), we also generalize the Kudla–Millson analytic theory of theta functions for indefinite quadratic forms to the case of torsion coefficients. This is joint work with Akshay Venkatesh. 
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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.