Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Observations of gravitational waves (GW) have the potential to unravel the mysteries of cosmic origins, constrain the equations of state of compact objects, and serve as a test of general relativity. To achieve these scientific goals, it is crucial to develop highly precise and accurate waveform templates to minimize systematic errors. My talk will focus on computing state-of-the-art effective two-body Hamiltonians and fluxes using techniques from quantum field theory and scattering amplitudes. These Hamiltonians and fluxes serve as fundamental building blocks for waveform templates, and dictate the accuracy of the waveform model. In particular, I will describe the effects of spinning and tidally deformed compact objects on evolution of the binary system. I will present computations of the linear-in-spin Hamiltonian at 4.5 post-Newtonian (PN) order, as well as the quadratic-in-spin Hamiltonian at 5PN order. Furthermore, I will describe oscillation modes of neutron stars (NS) induced by tidal interactions, particularly the fundamental-mode dynamical tides, which are expected to play a crucial role in constraining the NS equation of state in upcoming GW observing runs. I will discuss the computation of fluxes up to 2PN for adiabatic tidal interactions and effective Hamiltonians up to 3PN for both dynamic and adiabatic tidal interactions. The latter is particularly interesting as it requires introducing counterterms to remove divergences, leading to a renormalization group flow of the post-adiabatic Love number.
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
The S-matrix bootstrap is a non-perturbative framework that exploits general physical principles such as unitarity, analyticity, and crossing symmetry to constrain scattering amplitudes and gain insights into strongly interacting dynamics where perturbation theory fails. I will briefly review the state of the art of the modern bootstrap and motivate the need for a new framework that incorporates multi-particle unitarity. I will then describe the Atkinson-Mandelstam method and explain how deep-learning techniques enable its practical realization. Finally, I will present some of the results obtained using this approach.
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
We study scattering on the Coulomb branch of planar N=4 SYM.  At weak ‘t Hooft coupling scattering amplitudes can be computed using Feynman diagrams and the relevant degrees of freedom are quarks and gluons. At strong ‘t Hooft coupling the dynamics is captured by string scattering in flat space.  Dual conformal symmetry makes it possible to constrain the unitarity properties and the spectrum of the amplitude: bound states are encoded in the cusp anomalous dimension of a Maldacena-Wilson line with operators inserted at the cusp, which is fixed by integrability.  In this talk, we show how to combine dual conformal invariance, integrability, worldsheet bootstrap and the S-matrix bootstrap to explore scattering at finite ‘t Hooft coupling.  [Based on 2510.19909]
 
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Partial Differential Equations, Analysis and Geometry    A Conference in Honor of Sergiu Klainerman’s 75th Birthday    January 12-16 2026    at IHES – Marilyn and James Simons Conference Center    How to get to IHES
Registration is free but compulsory and open until December 31, 2025. 

Sergiu Klainerman, Eugene Higgins Professor of Mathematics at Princeton University, has made seminal contributions to nonlinear partial differential equations, analysis, differential geometry, and mathematical general relativity. He pioneered the vector field method for nonlinear wave equations, developed multilinear techniques for low-regularity analysis, and established landmark results on the stability of Minkowski space and Kerr black holes. His work has reshaped PDE, analysis, geometry, and relativity, training and inspiring generations of mathematicians.
Throughout his career, Sergiu Klainerman has received many distinctions, including:

Sloan Fellowship (1983–1985)

MacArthur Fellowship (1991–1996)

Guggenheim Fellowship (1997–1998)

Bôcher Memorial Prize, American Mathematical Society (1999)

Fellow of the American Academy of Arts and Sciences (1996)

Foreign Member of the French Academy of Sciences (2002)

Member of the U.S. National Academy of Sciences (2005)

Israel Gelfand Chair, IHÉS (2017–2019)

 
The conference will celebrate Sergiu Klainerman’s 75th birthday by bringing together experts to present recent advances in analysis, PDE, geometry, and general relativity, with the aim of fostering interaction across fields and engaging early-career researchers in these exciting developments.
Speakers:

Scott Armstrong (Sorbonne Université)
Thibault Damour (IHES)
Camillo De Lellis (IAS)
Patrick Gérard (Univ. Paris-Saclay, LMO)
Elena Giorgi (Columbia University)
Alexandru Ionescu (Princeton University)
Philip Isett (Caltech)
Jonathan Luk (Stanford University)
Sung-Jin Oh (UC Berkeley)
Duong Phong (Columbia University)

Richard Schoen (UC Irvine)

Sylvia Serfaty (Sorbonne Université)

Jacques Smulevici (Sorbonne Université)

Gigliola Staffilani (MIT)

Daniel Tataru (UC Berkeley)

Vlad Vicol (NYU)

Hong Wang (IHES & NYU)

Qian Wang (University of Oxford)

Pin Yu (Tsinghua University) 

Scientific committee:     Frank Merle (IHES & CY Cergy Paris Université), Jérémie Szeftel (Sorbonne Université)
Organizing committee:     Elena Giorgi (Columbia University), Markus Keel (University of Minnesota), Jérémie Szeftel (Sorbonne Université)
 

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 and Karol A. PENSON.
Speakers:

Cyril Banderier (LIPN)
Marek Bożejko (Wroclaw University)
Philippe Di Francesco (IPhT Saclay)
Vladimir Dotsenko (Université de Strasbourg)
Vladimir Fock (IRMA Strasbourg)
Oleg Kaikov (LIST, Saclay)
Arthemy Kiselev (University of Groningen)
Maxim Kontsevich (IHES)
Pierre-Vincent Koseleff (IMJ-PRG)
Gleb Koshevoy (IITP, Moscow)
Anastasia Matveeva (École polytechnique)
Thomas Müller (LIPN, Paris)
Hiroaki Nakamura (Osaka University)
Toshiki Nakashima (Sophia University Tokyo)
Lucas Pannier (Université de Versailles Saint-Quentin en Yvelines)
Karol Penson (LPTMC, Sorbonne Université)
Parham Radpay (Université Paris-Saclay)
Kilian Raschel (Université d’Angers)
Vladimir Roubtsov (Université d’Angers)
Thomas Simon (Université de Lille)
Reiko Toriumi (Okinawa Institute of Science and Technology)
 

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

 
 

Running Seminar
I will explain how to find Hodge points on the bases of Calabi-Yau families together with the respective Hodge cycles in their fibers by looking at their mod p reductions.
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Seed Seminar of Mathematics and Physics
I will present a concrete construction of 2d Ising partition functions on lattice, with non-abelian (more generally non-invertible) global symmetry. The construction realizes the Ising model as the boundary theory of a 3d symmetry topological field theory (SymTFT) with specific boundary conditions. Suitable choices of boundary conditions correspond to going to different topological sectors of the global symmetry or gauging arbitrary non-anomalous subsymmetry. Electric-magnetic type duality of the SymTFT results in dual descriptions of the Ising model that generalizes the Kramers-Wannier duality of Z/2Z symmetric Ising models.
 
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Seed Seminar of Mathematics and Physics
The conformal block expansion of correlation functions is a fundamental tool in the bootstrap program. Block computation can be related to a specific class of harmonic functions on the conformal group. We generalise this concept to the case of thermal conformal field theories and compute one-point blocks for spinning representations in three dimensions. Specifically, we derive a universal Casimir equation and solve it using recursion relations. Finally, we use the blocks in several examples to explore some features of OPE coefficients.
 
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Seed Seminar of Mathematics and Physics
Tensor network renormalization group (RG) is a powerful technique providing great control over the renormalization group flow both numerically and analytically. This talk will focus on the study of fixed points of tensor network RG maps in the context of classical lattice models (e.g., the Ising model). Studying fixed points allows one to retrieve information about phase transitions in a system, which motivates this research. I will first introduce basic tensor network concepts. Then, I will present some rigorous results about high- and low-temperature fixed points of lattice spin models (based on arXiv:2107.11464, 2210.06669, and 2401.04229). Finally, I will discuss the recent development that may grant access to the critical fixed points of lattice systems (based on arXiv:2408.10312).
 
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Seed Seminar of Mathematics and Physics
Anti-de Sitter space acts as an infra-red cutoff for asymptotically free theories, allowing interpolation between a weakly-coupled small-sized regime and a strongly-coupled flat-space regime. I will discuss this interpolation in the context of Yang-Mills theories in AdS from the perspective of boundary conformal theories and its implications for the confinement/deconfinement transition. We find indications that at the transition a singlet scalar operator becomes marginal, destabilizing the deconfined phase existing at a small size and leading to a confined phase that smoothly connects to flat space.
 
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Seed Seminar of Mathematics and Physics
Non-equilibrium dynamics of isolated quantum many-body systems plays an important role in contemporary theoretical physics research, from foundational questions on quantum statistical mechanics to the development of quantum technologies.I will provide a guided tour of a selection of results on thermalization and ergodicity breaking in quantum many-body dynamics, with an eye on mathematically rigorous studies, including (many) conjectures and (few) proven statements.  
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Seed Seminar of Mathematics and Physics
Our understanding of the behaviors appearing in statistical physics has been built firstly on the well-known Ising Model. Here, we will consider a disordered version of the one-dimensional Ising model: we will present and study the ferromagnetic Ising model on a line graph interacting with an external magnetic field, sampled from an i.i.d. distribution. We will be interested in the regime where the intensity of the disorder is fixed and the spin-spin interaction goes to infinity.
We will also introduce a continuous version of the model, which naturally arises from a weak disorder limit. For this continuous model, various quantities (such as the free energy) can be computed explicitely, thus yielding precise information on the typical configurations of the system.
The free energy of the discrete model can easily be expressed as the Lyapunov exponent of a random product of 2×2 matrices, which we estimate using Furstenberg’s theory: we will present recent results on the asymptotics of the free energy, in the regime we consider.
Furthermore, in both the discrete and the continuous models, we will caracterise the behaviour of the system at the level of configurations. In agreement with predictions in the physics literature, we will show that the configurations are typically close to one given configuration, determined by the environment (the external field), thus showing that the disorder is strongly relevant.
Our discussion will concern mainly the critical case, i.e., the case where the disorder is centered, but we may also address the non-critical case.
 
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