Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

The modular bootstrap has been a powerful tool for carving out the landscape of allowed two-dimensional conformal field theories (CFTs).  In this talk, I describe a complementary approach to standard modular bootstrap bounds: using modern machine learning strategies to actively search for CFT spectra that yield a valid torus partition function.  Using insights from statistical inference and a custom singular-value-based optimizer, I present evidence for an obstruction to finding CFTs with small central charge and large spectral gaps, and I speculate on what this might imply for the structure of the CFT landscape.  Along the way, I reflect on « centaur » approaches to theoretical physics, where human physicists and artificial intelligence collaborate to explore spaces of theories that would be difficult to navigate alone.
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
I will study planar, maximally supersymmetric 4d EFTs that reduce to ${mathcal N} = 4$ SYM at low energies and show that novel constraints arise from the six-point amplitude. By constructing the six-scalar amplitude and imposing supersymmetry together with standard tree-level factorization, assuming parity-even scalar contact terms, I find striking nonlinear relations among the four-point Wilson coefficients. These relations collapse much of the naive EFT parameter space. When combined with positivity bounds from unitarity and causality, the allowed region in Wilson-coefficient space shrinks to a thin sliver converging on the open-superstring Veneziano amplitude, strongly suggesting that maximal supersymmetry singles out the tree-level string answer. More broadly, the result shows that higher-point amplitudes contain qualitatively new bounds on the space of EFTs, and that the space of consistent quantum field theories may be much smaller than current four-point analyses suggest.
 
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Séminaire d’Analyse
Motivated by the phenomenon of duality for interacting particle systems we introduce two classes of Pfaffian kernels describing a number of Pfaffian point processes in the « bulk » and at the « edge ». Using the probabilistic method due to Mark Kac, we prove two  Szegő-type asymptotic expansion theorems for the corresponding Fredholm Pfaffians. The idea of the proof is to introduce an effective random walk with transition density determined by the Pfaffian kernel, express the logarithm of the Fredholm Pfaffian through expectations with respect to the random walk, and analyse the expectations using general results on random walks. We demonstrate the utility of the theorems by calculating asymptotics for the empty interval and non-crossing probabilities for a number of examples of Pfaffian point processes: coalescing/annihilating Brownian motions, massive coalescing Brownian motions, real zeros of Gaussian power series and Kac polynomials, and real eigenvalues for the real Ginibre ensemble. (Joint work with Will FitzGerald and Roger Tribe.)
 
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Séminaire d’Analyse
Invariant manifold theory is a fundamental tool in the study of local dynamics near invariant structures in smooth evolution systems. It ensures the existence of nonlinearly invariant structures from linear ones. The theory has been well developed for diffeomorphisms, ODEs, semilinear PDEs, and some quasilinear parabolic PDEs. However, it becomes subtle for quasilinear or more nonlinear PDEs due to regularity issues when there is no smoothing effect. In this talk, we consider a class of nonlinear PDEs whose linearizations satisfy certain energy estimates. We prove that the linear exponential dichotomy implies the existence of local stable/unstable manifolds of the equilibria. In particular the result applies to a class of nonlinear Hamiltonian PDEs including the capillary gravity water waves of one or two fluids, quasilinear wave and Schrödinger equations, KdV type equations, etc., for which the linear analysis is also discussed. Basically, for such systems under certain conditions, spectral instability implies the existence of stable and unstable manifolds, which in particular yields the nonlinear instability in rough Sobolev norms and/or the existence of solutions decaying in high Sobolev norms. This is a joint work with Jalal Shatah. 
 
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Schoenberg’s theorem on positive definite functions on spheres manifests in three distinct “avatars”: in the study of matrix preservers, the harmonic analysis of homogeneous spaces, and the representation theory of infinite-dimensional groups. I will discuss these connections, starting from the classical entrywise calculus of the Schur product theorem and extending to the asymptotic behavior of spherical functions on Olshanski spherical pairs.
As a geometric application, we will see how this framework recovers the linear programming bounds of Delsarte–Goethals–Seidel and Kabatiansky–Levenshtein for spherical codes, which in turn yield upper bounds for sphere packing densities. I will then extend Schoenberg’s classical framework to partially defined positivity preservers on discrete domains, and apply this machinery to the problem of soft thresholding for correlation matrices in high-dimensional statistics.
This is joint work with James Pascoe.
 
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Séminaire de géométrie arithmétique
A longstanding question in the theory of Shimura varieties concerns their perfectoidness at infinite level — a property that would reveal deep connections between étale and coherent cohomology. In this talk, we establish a criterion for perfectoidness via Sen theory, building on a new development of p-adic Hodge theory for general valuation fields that extends Tate’s foundational work on local fields. We further provide a conceptual explanation, based on the p-adic Simpson correspondence after Abbes-Gros, Liu-Zhu and Tsuji, for why Shimura varieties satisfy this criterion, at least in the case of modular curves. For general Shimura varieties, it follows through additional technical arguments due to Pan and Rodríguez Camargo. This yields the “pointwise perfectoidness” of Shimura varieties at infinite level, which suffices to establish the desired connection between different cohomologies. As an application, we show that integral completed cohomology groups vanish in higher degrees, thereby confirming a conjecture of Calegari and Emerton for arbitrary Shimura varieties.
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Black holes with sufficiently large initial charge and mass will Hawking-evaporate towards the extremal limit. The emission slows as the temperature approaches zero, but still reaches the point where a single Hawking quantum would make the object superextremal, removing the horizon. We take this semiclassical prediction at face value and ask: When the emission occurs, what is revealed?  Using a simple thin-shell model for the matter originally forming the black hole, we find that this matter *re-emerges* after the horizon is removed and subsequently expands back to large radius.  This expanding remnant has been bathed in the ingoing Hawking quanta during evaporation and presumably carries correlations with the outgoing quanta, offering the attractive possibility of studying information paradox issues in a setup where spacetime curvatures are globally small, so that quantum gravity is not required.
 
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Mathematics Inspired by Physics    A Conference in Honor of Yan Soibelman’s Contributions    June 1 & 2 2026    at IHES – Marilyn and James Simons Conference Center ; Léon Motchane Amphitheater   How to get to IHES
Registration is free but compulsory. 

Yan Soibelman, professor of mathematics at Kansas State University, has made influential contributions at the interface of geometry, algebra, and theoretical physics. His early work on quantum groups and braided categories helped shape modern interactions between representation theory and mathematical physics. His work is strongly inspired by ideas from quantum field theory and string theory, which he helps translate into rigorous mathematical frameworks.
In collaboration with Maxim Kontsevich, he has played a central role in the development of mirror symmetry, including various fundamental results in the theory of operads and A  ͚ categories. He also introduced key concepts such as motivic Donaldson–Thomas invariants, the Kontsevich–Soibelman wall-crossing formula, and cohomological Hall algebras. His work has had a lasting impact on areas where physics drives new mathematical insights.
 
The conference will celebrate Yan Soibelman’s contributions by bringing together experts to present recent advances & foster interaction across fields as well as engaging early-career researchers in these exciting developments.
Speakers:

Veronica Fantini, Laboratoire de Mathématique d’Orsay

Mikhail Kapranov, Kavli Institute

Bernhard Keller, Institut de mathématiques Jussieu-Paris Rive Gauche

Maxim Kontsevich, IHES

Pierre Schapira, Institut de mathématiques Jussieu-Paris Rive Gauche

Olivier Schiffmann, CNRS, Laboratoire de Mathématiques d’Orsay

Alexander Soibelman, IHES

Yan Soibelman, Kansas State University

Bruno Vallette, Université Sorbonne Paris Nord 

 
Organizing committee:     Mikhail Kapranov, Kavli Institute · Maxim Kontsevich, IHES
 

The parallel transport construction can be used to produce an equivalence of categories between the category of representations of the fundamental group of a smooth connected manifold and the category of flat bundles over this manifold. I will discuss an analogue of this construction when the field of real numbers is replaced by the field of p-adic numbers. Given a smooth rigid space X over ℚp, consider the ring D of differential operators on the base change of X to Fontaine’s period ring BdR+. Let Dt be the subalgebra spanned by functions and vector fields multiplied by a uniformizer t in BdR+. Thus, Dt is an algebra over BdR+, whose mod t reduction is the commutative algebra of functions on the cotangent space, and which is isomorphic to D after inverting t. The category of modules over Dt can be twisted by any μp∞ gerbe over the cotangent space. I will construct a functor from the category of étale BdR+-local systems on XCp to the category of modules over Dt twisted by the Simpson gerbe. The composition of this functor with the mod t reduction recovers the p-adic Simpson functor of Bhatt and Zhang.
 
This is a joint work in progress with Bhargav Bhatt, Ben Heuer and Alexander Petrov.
 
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