Gluing the opposite sides of a square gives a flat torus: a torus endowed with a flat metric induced by the Euclidean metric on the square. Similarly, one can produce higher genus surfaces by gluing parallel sides of several squares. These « square-tiled surfaces » inherit from the squares a flat metric with conical singularities. In this talk we will present several recent results and conjectures on the large genus asymptotics of these surfaces, and more generally of some families of flat surfaces (joint work with V. Delecroix, P. Zograf and A. Zorich). We will also see how these results can be interpreted in the language of closed curves on surfaces. We will finish with some recent results joint with E. Duryev and I. Yakovlev that should allow to generalize these results to a larger family of flat surfaces.
 

Séminaire de géométrie arithmétique
The mod-$p$ cohomology of equi-$p$-saturable pro-$p$ groups has been calculated by Lazard in the 1960s. Motivated by recent considerations in the mod-$p$ Langlands program, we consider the problem of extending his results to the case of compact $p$-adic Lie groups $G$ that are $p$-saturable but not necessarily equi-$p$-saturable: when $F$ is a finite extension of $mathbb{Q}_p$ and $p$ is sufficiently large, this class of groups includes the so-called pro-$p$ Iwahori subgroups of $SL_n(F)$. In general, using the work of Serre and Lazard one can write down a spectral sequence that relates the mod-$p$ cohomology of $G$ to the cohomology of its associated graded mod-$p$ Lie algebra $mathfrak{g}$. We will discuss certain sufficient conditions on $p$ and $G$ that ensure that this spectral sequence collapses. When these conditions hold, it follows that the mod-$p$ cohomology of $G$ is isomorphic to the cohomology of the Lie algebra $mathfrak{g}$.
 
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

In this talk, I will show how to construct a holographic effective theory for the leading-twist multi-particle operators for $O(2)$ CFT in $d=3$ and $d=4-epsilon$. For $d=4-epsilon$ Wilson-Fisher fixed point. We obtain the Hamiltonian of the theory and show that it correctly reproduces all the dimensions at order ${mathcal O}(epsilon^2)$ of the leading twist operators for all values of the charge $Q$ and spin $J$. For $d=3$ strongly coupled $O(2)$ CFT, we find excellent agreement with $Q=3,4$ bootstrap data and inversion formula.
 
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.
 

Running Seminar
 
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
I will discuss the high-energy, small-angle limit of two-body classical gravitational scattering, focusing on the tower of multi-H diagrams that govern the leading logarithmic behavior. First, I will show that the recently developed SCET forward-scattering framework for gravity is fully equivalent to the multi-Regge expansion of the classical amplitude, reproducing exactly the s-channel multi-H diagrams. I will then compute the single-H diagram at two loops and the double-H diagrams at four loops, matching onto the classical eikonal phase in the ultrarelativistic limit. Finally, using dispersion relations, we establish a novel link between the high-energy logarithmic terms in the real and imaginary parts of the eikonal phase at 5PM order.
 
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Perturbative field theory calculations are essential for precision predictions in collider and gravitational-wave physics. One of the major bottlenecks in such calculations is integration-by-parts (IBP) reduction of the underlying Feynman integrals. In this talk, I will argue that IBP reduction can be simplified by exploiting the infrared singularity structure encoded in the Landau equations. More precisely, I will show that the IBP syzygy module decomposes as a sum over the Fitting ideals associated with the individual components of the Landau locus. This decomposition provides an efficient method for constructing syzygies and suggests universality of solutions among integral topologies sharing the same infrared structure.
 
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

I will report on an ongoing project in collaboration with Yannick Guedes Bonthonneau and Tobias Weich. The goal of this work is to define a natural spectrum associated with Anosov representations, consisting of complex hypersurfaces in the complexified dual Cartan subalgebra. The leading hypersurface corresponds to a well-known object in the literature — the so-called critical hypersurface of the representation. To some extent, this spectrum generalizes a similar notion in the rank-one case, known as the set of Pollicott-Ruelle resonances (and the leading resonance), which is known to encode the exponential decay of correlations, among other properties. I will describe the main consequences of this spectral approach, namely the meromorphic extension (to the full complexified dual Cartan subalgebra) of dynamical zeta functions and Poincaré series associated with the representation. If time permits, I will discuss specific values of these functions, the sharp quantitative decay of correlations for the refraction flow, and the perspectives for future work.
 

I will present several results on the topology of closed manifolds of dimension at least 4 that admit a (real) properly convex projective structure, all related to a vanishing theorem of Kobayashi from 1984 for the rational Pontryagin classes. In arbitrary dimensions, I will outline a classification of locally symmetric manifolds admitting properly convex projective structures. Focusing on dimension 4, I will then present a result on the geometric decomposition which is the analogue of a theorem of Benoist in dimension 3, and the construction of examples that realize all possible positive values of the Euler characteristic. Based on joint work with Stefano Riolo and Leone Slavich.
 

Running Seminar
In abstract Hodge theory, Deligne’s delta splitting measures how far a mixed Hodge structure is from being split as a real mixed Hodge structure. An allied notion, developed by S. Bloch, R.Hain et al., is that of a height for a special class of mixed Hodge structures called Biextensions.
The idea of a Biextension is closely related to algebraic cycles homologous to zero. Given two such cycles in complementary codimensions in an ambient smooth and projective variety, a certain cohomology group associated to the pair provides an example of a Biextension-type mixed Hodge structure.  The height associated with such a Biextension has been well studied and has been an active area of research for the past few decades.
 In an ongoing project, the speaker, along with J. I. Burgos Gil and G. Pearlstein, has developed a theory of mixed Hodge structures and heights associated with Bloch’s higher cycles, that generalizes the above study of Biextensions (doi.org/10.1112/plms.12443 and arXiv:2410.17167v2 [math.AG]).
 In the talk, I will explain the current state of the art of this project after reviewing the established theory.
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.