Au niveau microscopique, un gaz est une collection de particules neutres en interaction. Le très grand nombre de degrés de libertés et la sensibilité du système à de très petites perturbations font qu’il est essentiellement impossible d’en prédire la dynamique de façon déterministe.
A la fin du XIXème siècle, Boltzmann a proposé de décrire le comportement du gaz de façon alternative par une approche statistique. Une question naturelle est alors de savoir si l’hypothèse d’indépendance statistique qui sous-tend ce modèle est compatible avec la dynamique microscopique et en quel sens l’équation de Boltzmann en est une bonne approximation.
Ce cours donnera quelques éléments de réponse à cette question, dans le cadre simplifié d’interactions par contact.
1. L’équation de Boltzmann, l’hypothèse de chaos et le théorème H
2. Loi des grands nombres pour la dynamique des sphères dures
3. Corrélations, clusters dynamiques
4. Fluctuations et grandes déviations pour la dynamique des sphères dures
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At the microscopic level, a gas is a collection of interacting neutral particles. The very large number of degrees of freedom and the sensitivity of the system to very small perturbations mean that it is essentially impossible to predict its dynamics deterministically.
At the end of the 19th century, Boltzmann proposed describing the behaviour of gas in an alternative way, using a statistical approach. A natural question is whether the assumption of statistical independence that underlies this model is compatible with microscopic dynamics and in what sense the Boltzmann equation is a good approximation.
This course will provide some answers to this question, within the simplified framework of contact interactions.
1. The Boltzmann equation, the chaos hypothesis and the H theorem
2. Law of large numbers for the dynamics of hard spheres
3. Correlations, dynamic clusters
4. Fluctuations and large deviations for the dynamics of hard spheres
 

Au niveau microscopique, un gaz est une collection de particules neutres en interaction. Le très grand nombre de degrés de libertés et la sensibilité du système à de très petites perturbations font qu’il est essentiellement impossible d’en prédire la dynamique de façon déterministe.
A la fin du XIXème siècle, Boltzmann a proposé de décrire le comportement du gaz de façon alternative par une approche statistique. Une question naturelle est alors de savoir si l’hypothèse d’indépendance statistique qui sous-tend ce modèle est compatible avec la dynamique microscopique et en quel sens l’équation de Boltzmann en est une bonne approximation.
Ce cours donnera quelques éléments de réponse à cette question, dans le cadre simplifié d’interactions par contact.
1. L’équation de Boltzmann, l’hypothèse de chaos et le théorème H
2. Loi des grands nombres pour la dynamique des sphères dures
3. Corrélations, clusters dynamiques
4. Fluctuations et grandes déviations pour la dynamique des sphères dures
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
At the microscopic level, a gas is a collection of interacting neutral particles. The very large number of degrees of freedom and the sensitivity of the system to very small perturbations mean that it is essentially impossible to predict its dynamics deterministically.
At the end of the 19th century, Boltzmann proposed describing the behaviour of gas in an alternative way, using a statistical approach. A natural question is whether the assumption of statistical independence that underlies this model is compatible with microscopic dynamics and in what sense the Boltzmann equation is a good approximation.
This course will provide some answers to this question, within the simplified framework of contact interactions.
1. The Boltzmann equation, the chaos hypothesis and the H theorem
2. Law of large numbers for the dynamics of hard spheres
3. Correlations, dynamic clusters
4. Fluctuations and large deviations for the dynamics of hard spheres
 

12e séminaire ITZYKSON : Problèmes spectraux quantiques en physique mathématique

Le 12e séminaire Itzykson est organisé par Sylvain Ribault (IPhT Saclay) et Pierre Vanhove (IPhT Saclay). 
Depuis une dizaine 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 en français et deux ou trois exposés spécialisés en français ou en anglais.
Le prochain Séminaire Itzykson portera sur des progrès récents spectaculaires sur les relations entre des problèmes spectraux quantiques et des problèmes de physique mathématique. Ces progrès conduisent à des résultats exacts pour la théorie spectrale de nouvelles familles d’équations différentielles et d’équations aux différences. 
Un cours et deux exposés auront lieu dans la journée, présentés par : 

Alba Grassi, Université de Genève
Yilber Fabian Bautista, IPhT Saclay
Alessandro Tanzini, SISSA Trieste

L’inscription est gratuite mais nécessaire et sera possible jusqu’au 20 novembre 2024. 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.

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Recent advances in modelling unbound binary black hole interactions have been driven by the application of scattering amplitude methods to generate results within the post-Minkowskian (PM) expansion. However, this expansion breaks down when approaching the strong-field where the large curvature effects become non-negligible. In this talk, I will show how numerical information from self-force (SF), an expansion in the small mass ratio of the system, can inform higher-order coefficients in the PM expansion. I will also show how a single point of SF scattering data can be used to resum the PM series, providing accurate predictions for scattering angles across all separations. Additionally, I will present results from unbound numerical relativity simulations, where the full Einstein field equations are solved for comparable mass systems, and compare these with predictions from PM-informed effective one body models.
 
 
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The Summer School will be held at IHES from  June 23 to July 4, 2025. 
The summer school is a StatPhys29 satellite event
2025 IHES Summer School – Statistical Aspects of Nonlinear Physics
Statistical mechanics, non linear physics and mathematics have often progressed hand in hand, mutually enriching themselves by exchanging key questions and methods. This summer school will be organized around these interactions, with the aim of deepening them and extending them to current research questions. We have identified four active and quickly advancing topics : Random interfaces, Disordered landscapes and AI, Long-range interactions, and Active matter. Each one will be addressed simultaneously by two internationally renowned lecturers, a physicist and a mathematician. This original set-up for the summer school organization will provide two different points of view on the same topic and the tools to bridge them. We aim to bring together attendees from physics and mathematics, to provide them with opportunities to broaden their perspectives, from experimental physics to theoretical physics and mathematics, and to expand their scientific network.
Four courses given jointly by a physicist and a mathematician on the following themes :

Collective behavior: from crowd movements to active matter : Bertrand MAURY (LMO) & Julien TAILLEUR (MIT)
Disorder Landscapes, out of equilibrium dynamics and AI: Gérard BEN AROUS (New York University) & Giulio BIROLI (LPENS)
Long-range interactions: Satya N. MAJUMDAR (LPTMS) & Sylvia SERFATY (Sorbonne Université and Courant Institute of Mathematical Sciences)
Random interfaces: Ivan CORWIN (Columbia University) & Kazumasa TAKEUCHI (The University of Tokyo)

This summer school is open to everybody. Priority will be given to PhD students and postdoctoral fellows but applications from more senior researchers are also welcome.
The courses are designed for a mixed audience of physicists and mathematicians. The aim is to provide an introduction to a wide range of topics, and to help students develop their skills and knowledge. 
Deadline for applications: February 23, 2025 

2025 IHES SUMMER SCHOOL

Theme: Recent rigidity results for discrete subgroups of Lie groups and their actions on manifolds, at the intersection of dynamics with Lie theory and geometry. 
The Summer School will be held at the Institut des Hautes Études Scientifiques (IHES) from July 7-18, 2025. IHES is located in Bures-sur-Yvette, south of Paris (40 minutes by train from Paris) – Access map

Recently there has been remarkable progress on several important problems broadly centered around the study of discrete subgroups of Lie groups. The primary goal of this summer school is to allow young reseachers to come together and learn about a number of these exciting developments. 
Activities will be centered around lecture series by established experts known both for their strong contributions to the field and for the high quality of their mathematical exposition. We also plan to foster an environment where these young mathematicians are able to learn from each other and have opportunities to begin new collaborations that will drive the future of the subject.
The programme of the school will consist of nine mini-courses each ranging between 3 to 5 hours of lecture, and will include evening problem sessions.
Organizing Committee/Scientific Committe: David Fisher (Rice University), Fanny Kassel (CNRS & IHES), Ralf Spatzier (University of Michigan) and Matthew Stover (Temple University).
This school is open to everybody but intended primarily for young participants, including Ph.D. students and postdoctoral fellows. 
Application is open until March 16, 2025

Mini-courses speakers:

Simion Filip, University of Chicago

Homin Lee, Northwestern University

Sam Mellick, Jagiellonian University and Amanda Wilkens, Carnegie Mellon University 

Daniel Monclair, Université Paris-Saclay

Maria Beatrice Pozzetti, Universitá di Bologna

Roman Sauer, Karlsruher Institut für Technologie
Barbara Schapira, IMAG, Université de Montpellier
Antoine Song, California Institute of Technology
Nattalie Tamam, Imperial College London

This is an IHES Summer School organized in partnership with the following institutions and sponsors:

Probability and analysis informal seminar
We start by reviewing the classical Sherrington-Kirkpatrick (SK) model. In this model, +1/-1-valued spins interact with each other subject to random coupling constants. The covariance of the random interaction is quadratic in terms of spin overlaps. Parisi proposed the celebrated variational formula for the limit of free energy of the SK model in the 80s, which was later rigorously verified in the works by Guerra and Talagrand. This formula has been generalized in various settings, for instance, to vector-valued spins, by Panchenko. However, in these cases, the convexity of the interaction is crucial. In general, the limit of free energy in non-convex models is not known and we do not have variational formulas as valid candidates. Here, we report recent progress through the lens of the Hamilton-Jacobi equation. Under the assumption that the limit of free energy exists, we show that the value of the limit is prescribed by a characteristic line; and the limit (as a function) satisfies an infinite-dimensional Hamilton-Jacobi equation « almost everywhere ». This talk is based on a joint work with Jean-Christophe Mourrat.​
 
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In this talk, we bootstrap various objects in planar maximally supersymmetric Yang- Mills theory. Focusing on the four-point correlation function of stress-tensor, we first demonstrate why the conventional bootstrap approach fails and new techniques are required. Next, we introduce a set of sum rules that are tailored for this problem as they are sensitive only to single-traces in the OPE expansion. Integrability enters at this stage and provides information on the spectrum of these operators. Their OPE coefficients, however, remain elusive. We then discuss how these sum rules can be employed in numerical bootstrap to nonperturbatively bound the OPE coefficients, the four-point correlation function and the energy-energy correlator. We show, for the first time, rigorous non-perturbative results for the planar OPE coefficient of single-trace operators as well as the correlation function at various points in cross-ratio space. Additionally, focusing on the energy-energy correlator (EEC), we present rigorous bounds for its spin 2 and spin 3 Legendre coefficients as well as the full EEC function at various angles. These results were obtained for a wide range of  t’Hooft couplings, highlighting the power of the bootstrap in probing non-perturbative aspects of planar N=4 SYM theory.
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
In conventional world-line formalism for spinning binaries in general relativity, one assumes that the dynamical degrees of freedom for spin are the completely captured by the rest frame canonical spin. A spin supplementary condition (SSC) is then necessary to remove redundancies. We study this problem from an amplitude-based field theory perspective. In higher spin field theories, it is notoriously difficult to impose transverse and traceless conditions when interactions are included. We take an alternative approach and keep the additional degrees of freedom. We see that for generic Wilson coefficients, we obtain a system with a dynamical mass dipole that has physical effect starting at the quadrupole level. It will decouple when we choose special values for Wilson coefficients, and we land back on the dynamics of conventional spinning binaries. The situation is very similar to a symmetry breaking in the classical limit. We also construct a world-line Lagrangian and a classical effective Hamiltonian that completely match the physics mentioned above, which incorporates a dynamical mass dipole as the additional dynamical degree of freedom. The mass dipole has physical effects, and its significance is a question for phenomenology. On the other hand, the dipole can be removed by an emergent world-line shift symmetry when Wilson coefficients take special values. From this perspective, our formalism can simplify the calculation for conventional spinning binaries, as the SSC constraint can be effectively relaxed.
 
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Given a compact hyperbolic surface together with a suitable choice of orthonormal basis of Laplace eigenforms, one can consider two natural spectral invariants: 1) the Laplace spectrum $Lambda$, and 2) the 3-tensor Cijk representing pointwise multiplication (as a densely defined map L2 x L2  $to$ L2) in the given basis. Which pairs ($Lambda$,C) arise this way? Both $Lambda$ and C are highly transcendental objects. Nevertheless, we will give a concrete and almost completely algebraic answer to this question, by writing down necessary and sufficient conditions in the form of equations satisfied by the Laplace eigenvalues and the Cijk. This answer was suggested by physicists Kravchuk, Mazac, and Pal, who introduced these equations (in an equivalent form) as a rigorous model for the crossing equations in conformal field theory.
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
In this talk, I will show how one can study gravitational perturbations from the near-horizon region of extremal and near-extremal rotating black holes in a general higher-derivative extension of Einstein gravity. I will explain how the near-horizon Teukolsky equation is modified via a correction to the angular separation constant. The near-horizon region also provides constraints on the form of the full modified Teukolsky radial equation, which serve as a stepping stone towards the study of quasinormal modes of near-extremal black holes. In the second part of the talk, I will show how this EFT can be constrained, motivated by preserving two fundamental properties of GR: gravitational waves are non-birefringent, and black hole quasinormal modes are isospectral. This leads to a novel class of EFT extensions, which remarkably, coincides with predictions from string theory and implies a previously unknown feature of string theory effective actions.
 
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We use Teichmüller theory to construct a new geometric model for the classifying space of the mapping class group of a three-dimensional handlebody. Two consequences are obtained: (i) Chan-Galatius-Payne have recently shown that the homology of Kontsevich’s commutative graph complex injects into the homology of the mapping class groups of surfaces, producing an enormous amount of highly unstable homology classes. We show that this homomorphism factors through the homology of the corresponding handlebody mapping class groups. (ii) The handlebody mapping class group is a virtual duality group in the sense of Bieri-Eckmann, with dualizing module given by a certain complex of nonsimple disk systems; the analogous result for mapping class groups of surfaces is a theorem of Harer. (Joint with Louis Hainaut and with Ric Wade.) 
 
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