We give an asymptotic formula for the number of common perpendiculars with length tending to infinity between two divergent geodesics in finite volume real hyperbolic manifolds, presenting a surprising non-purely exponential growth. We apply this result to count ambiguous geodesics in the modular curve, recovering results of Sarnak, and to prove a conjecture of Motohashi on the binary additive divisor problem in imaginary quadratic number fields. This is joint work with Jouni Parkkonen.
 

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
The Robinson–Trautman (RT) spacetime is an algebraically special solution of the vacuum Einstein equations. I will show that, in the absence of radiation, it corresponds to the vacuum sector of Euclidean Liouville theory. Moreover, upon linearization, the solution can be expressed as a superposition of specific quasi-normal modes of the Schwarzschild black hole. Finally, nonlinear effects—including memory—and the emergence of resonant modes in the radiation will also be discussed.
 
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We discuss techniques (Cordoba argument, projection theory) to prove volume bounds on union of tubes in R2 and R3, with applications to the Kakeya problem. This is joint work with Josh Zahl.

We discuss techniques (Cordoba argument, projection theory) to prove volume bounds on union of tubes in R2 and R3, with applications to the Kakeya problem. This is joint work with Josh Zahl.

We discuss techniques (Cordoba argument, projection theory) to prove volume bounds on union of tubes in R2 and R3, with applications to the Kakeya problem. This is joint work with Josh Zahl.

In pure SU(n) 4D QCD, i.e. SU(n) Yang-Mills theory without matter, there exists stable long fluxtube strings which carry a 1-form symmetry charge. Over the past decade, there has been increasing evidence from lattice calculations that the worldsheet theories of such QCD strings contain a massive pseudoscalar (axion), at least when n>2. This has so far been puzzling from the perspective of holographic realizations of strings in confining gauge theories. In this talk, I will show how such axions appear naturally in the realization of 4D N=1 pure QCD from M-theory on non-compact G2 orbifolds. I will also show that this picture predicts that QCD string axions exist only if the gauge group is SU(n) (n>2), SO(4n+2), or E6 (or a quotient/double-cover thereof), and why I expect this pattern to hold for non-susy pure QCD as well. This pattern could be tested in future lattice studies of QCD strings for gauge groups of B, C, D, and E-type. 
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Elucidating the nature of dark matter, dark energy, and dynamics of the early universe stand as major challenges of modern cosmology and particle physics. I will present a new program of addressing these challenges with spectroscopic galaxy surveys. This program builds on effective field theory (EFT) ideas borrowed from particle physics. The application of the EFT to large-scale structure allows for sub-percent precision analytic understanding of galaxy clustering on quasi-linear scales and provides an unmatched flexibility in testing new physics scenarios beyond the standard cosmological model. I will share some results of this program that include new measurements of fundamental cosmological parameters and novel constraints on dark energy, dark matter, and the physics of the early universe.
 
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This one-day workshop is organised jointly by Huawei and IHES, as a part of the IHES-Huawei partnership. The aim of the workshop is to bring together prominent voices from academia and industry to explore the evolving role of causal reasoning in artificial intelligence. The workshop will deliver meaningful dialogue around two major directions. The first one is theory-driven causal modelling, which focuses on theoretical approaches, frameworks, and tools for understanding causality, emphasizing the development of rigorous methods to identify, estimate, and interpret causal relationships. The second topic is machine learning with causal AI and its applications, which integrates machine learning and deep learning techniques to improve causal discovery, causal inference, causal representation learning and their corresponding application fields.
INVITED SPEAKERS: 

BOWDEN Jack (Exeter University, UK)
CADEI Riccardo (EPFL, Switzerland)
FUNG Pascale (HKUST & Visiting Professor at the Central Acad. of Fine Arts in Beijing)
HENCKEL Leonard (Univ. College, Dublin, UK)
LI Haoxuan (Peking University)
LIMNIOS Myrto (EPFL, Switzerland)
TIAN Jin (MBZUAI, Abu Dhabi)
ZHOU Hong (Huawei)

 
 

 
 
Organisers: Keshuang Li (Huawei), Keli ZHANG (Huawei)

13e séminaire ITZYKSON : Bootstrap conforme et géométrie spectrale

Le 13e séminaire Itzykson est organisé par Sylvain Ribault (IPhT Saclay), Slava Rychkov (IHES) 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 et deux ou trois exposés spécialisés (en français ou en anglais selon le choix des orateurs).
Le prochain séminaire Itzykson portera sur la théorie conforme des champs, et ses liens avec la géométrie spectrale, et la théorie des nombres. Ces sujets sont reliés par la possibilité d’appliquer une même méthode: le bootstrap conforme. Le séminaire donnera des perspectives mathématiques et physiques sur des résultats récents, notamment au sujet des spectres des variétés hyperboliques, des fonctions L en théorie des nombres, et des spectres des théories conformes.
Un cours et deux exposés auront lieu dans la journée, présentés par : 

Dalimil Mazáč, IPhT Saclay & IHES

Frédéric Naud, Sorbonne Université, IMJ-PRG
Balt van Rees, CPHT, École polytechnique

L’inscription est gratuite mais nécessaire et sera possible jusqu’au 8 octobre 2025. 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.

We present a new structure on the first Galois cohomology of families of symplectic self-dual $p$-adic representations of $G_{Q_p}$ of rank two. This is a functorial decomposition into free rank one Lagrangian submodules encoding Bloch-Kato subgroups and epsilon factors, mirroring an underlying symplectic structure. This local sign decomposition has local as well as global applications, including compatibility of the Mazur-Rubin arithmetic local constants and epsilon factors, and new cases of the parity conjecture. It also leads to a formulation and proof of an analogue of Rubin’s conjecture over ramified quadratic extensions of $Q_p$, which initiates an integral Iwasawa theory for CM elliptic curves at primes of additive reduction. (Joint with A. Burungale, K. Nakamura, and K. Ota.)
 
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The purpose of this talk is to give fine limit theorems for the norm llgn…g1ll of a  product of random matrices, under some conditioning. These limit theorems are stated in analogy with the case of sums X1+…+Xn of real random variables. This is joint work with Ion Grama and Hui Xiao.
 

Let X be a pinched Cartan-Hadamard manifold, and Y a symmetric space of non-compact type. We define a notion of stability for coarse Lipschitz maps f : X → Y, and show that every stable map from X to Y is at bounded distance from a unique harmonic map. As an application, we extend any positive quasi-symmetric map from RP1 to the flag variety of SL(n,R), to a harmonic map from H2 to the symmetric space of SL(n,R). This allows us to define a universal Hitchin component in the style suggested by Labourie and Fock-Goncharov. This is all joint work with Peter Smillie.