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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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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An introduction to examples of SL2(R) – invariant subvarieties V of the moduli space of holomorphic 1-forms, Omega Mg , and their connections to topology, Hodge theory and algebraic geometry.

Introduction of translation surfaces (definitions and examples) and their moduli spaces, period coordinates, SL(2,R)-action (examples: pseudo-Anosov), Kontsevich-Zorich cocycle (examples of concrete matrices via Thurston-Veech and/or Rauzy-Veech algorithm), some applications (of Zorich phenomenon in Delecroix-Hubert-Lelievre and of Lyapunov exponents in Kappes-Moeller).

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

The work discussed is joint with André Belotto da Silva, Michael Temkin and Jaroslaw Wlodarczyk.
Given a subvariety X of a nonsingular complex variety Y carrying a monomial foliation F, we construct an embedded resolution of singularities of X that is aligned with the foliation F, solving a problem of Belotto da Silva. This in particular implies resolution of singularities of singular integrable foliations.
 
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Probability and analysis informal seminar
The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergoned by certain Markov processes in the limit where the number of states tends to infinity. Discovered forty years ago in the context of card shuffling, it has since then been established in a variety of contexts, including random walks on graphs and groups, high-temperature spin systems, or interacting particles. Nevertheless, a general theory is still missing, and identifying the general mechanisms underlying this mysterious phenomenon remains one of the most fundamental problems in the area of mixing times. In this talk, I will give a self-contained introduction to this fascinating question, and then describe a new approach based on entropy and curvature.
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A Teichmüller curve V in Mg is an isometrically immersed algebraic curve in the moduli space of Riemann surfaces. These rare, extremal objects lie at the nexus of algebraic geometry, number theory, complex analysis and surface topology. We will discuss some ideas behind the known constructions of Teichmüller curves that have been discovered over the past 30 years, and a selection of open problems.