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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Séminaire de géométrie arithmétique
For an absolutely unramified extension $K/mathbb{Q}_p$ with perfect residue field, by the works of Fontaine, Colmez, Wach and Berger, it is well known that the category of Wach modules over a certain integral period ring is equivalent to the category of lattices inside crystalline representations of $G_K$ (the absolute Galois group of $K$). Moreover, by the recent works of Bhatt and Scholze, we also know that lattices inside crystalline representations of $G_K$ are equivalent to the category of prismatic $F$-crystals on the absolute prismatic site of $O_K$, the ring of integers of $K$. The goal of this talk is to present a direct construction of the categorical equivalence between Wach modules and prismatic $F$-crystals over the absolute prismatic site of $O_K$. If time permits, we will also mention a natural generalisation of these results to the case of a « small » base ring and intended application (work in progress).
 
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Combinatorics and Arithmetic for PhysicsThe meeting focuses on questions of discrete mathematics and number theory, emphasizing computability. Problems are drawn mainly from theoretical physics: renormalization, combinatorial physics, geometry, evolution equations (commutative and noncommutative), or related to its models, but not only. 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, Sergei NECHAEV, and Karol A. PENSON.
Speakers:

Nicolas Behr, CNRS, Université de Paris, IRIF
Joseph Ben Geloun, LIPN-Paris XIII
Lara Bossinger, IM UNAM, Oaxaca & IAS, Princeton
Marek Bozejko, Wroclaw University
Stéphane Dartois, Université Paris Saclay, CEA
Jehanne Dousse, Université de Genève
Gérard H.E. Duchamp, LIPN, Université Paris Nord
Vladimir Fock, IRMA, Strasbourg
Darij Grinberg, Drexel University
Dimitry Gurevich, IITP, Moscow
Yuki Kanakubo, Ibaraki University
Arthemy Kiselev, University of Groningen
Maxim Kontsevich, IHES
Gleb Koshevoy, IITP, Moscow
Toshiki Nakashima, Sophia University Tokyo
Mohamed Ouerfelli, Université Paris Saclay, CEA
Karol A. Penson, LPTMC, Sorbonne Université
Gleb Pogudin, LIX, Ecole polytechnique
Markus Reineke, Ruhr University Bochum
Ioannis Vlassopoulos, Athena Research Center
 

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

Representations, Probability, and Beyond: A Journey into Anatoly Vershik’s World Workshop in memory of A.M. Vershik
November 18-19, 2024, Mikhail Gromov (IHES & NYU), Sergei Nechaev (LPTMS Paris-Saclay) and Volodya Rubtsov (Univ. Angers) organize a two-day workshop devoted to the memory of Anatoly Vershik, who passed away earlier this year.
Anatoly Vershik (1933-2024) was a Russian mathematician who made important contributions in several fields of mathematics. In particular, he is renowned for his joint work with Sergei V. Kerov on the theory of representations of infinite symmetric groups and on applications of the longest strictly increasing subsuite problem in group theory. 
 
 
Invited Speakers:

Alexander BARVINOK (Univ. of Michigan)
Alexey BORODIN (MIT)
Alexander CHERVOV (Institut Curie)
Anna ERSCHLER (Sorbonne Univ.)
Sergey FOMIN (Univ. of Michigan)
Mikhail GROMOV (IHES & NYU)
Vadim KAIMANOVICH (Univ. of Ottawa)
Andrey MALYUTIN (St. Petersburg State Univ.)
Tatiana NAGNIBEDA (Univ. Genève)
Sergei NECHAEV (LPTMS Paris-Saclay)
Andrey OKOUNKOV (Princeton Univ.)
Grigorii OLSHANSKII (IITP, Moscow)
Leonid PASTUR (King’s College London)
Fyodor PETROV (St. Petersburg State Univ.)
Volodya RUBTSOV (Univ. d’Angers)
Natalia TSILEVICH (Bar Ilan University)

 

Probability and analysis informal seminar
The Laplacian is a central operator in the analysis of surfaces (and life in general). In this talk, we investigate how small its small eigenvalues can be, giving a sharp, quadratic bound on the k-th eigenvalue of a surface in terms of k, the surface’s genus g, and its global geometry via the injectivity radius. The techniques involve extremal length, spectral embedding, and volume arguments.Joint work with Guy Lachman and Asaf Nachmias, based on the paper: https://arxiv.org/abs/2407.21780For an exposition and overview of the paper, see here:

New paper on arXiv: A sharp lower bound on the eigenvalues of surfaces

 
 
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