Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
In this seminar, I will present the formalism we developed to solve analytically the Teukolsky equation and compute observables at first order in Self Force for the scattering problem, by combining a low-velocity (Post-Newtonian) and a large impact parameter (Post-Minkowskian) expansion. In particular, we generalize the usual techniques employed for studying bounded orbits, which presents a distinctive discrete frequency spectrum, in order to include the continuous Fourier spectrum of the unbound motion. Interestingly, this extension produces a rich mathematical structure on the non-local, logarithmic-in-frequency, sector.
I will briefly recap the application of these techniques on the scattering of a scalar charge, then I will present some preliminary results on the gravitational problem.
 
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Séminaire de géométrie arithmétique
I will present a new geometric perspective on the p-adic monodromy theorem of André, Kedlaya, and Mebkhout, which is based on the study of vector bundles on the analytic de Rham stack of the Fargues–Fontaine curve. I will then outline some applications to the p-adic Hodge theory of rigid-analytic varieties.   
This is based on joint work in progress with Anschütz, Le Bras, and Rodriguez Camargo. 
 
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Running Seminar
Given a hyperbolic knot K, state integrals are convergent integrals of products of Faddeev’s quantum dilogarithm associated with certain triangulations of S3K. Their asymptotic expansions are divergent power series conjectured to be resurgent and Borel-Laplace summable by Garoufalidis, Gu and Mariño. In this talk, I will prove this conjecture for the knots 41 and 52. This is based on a joint project with C. Wheeler, arXiv:2410.20973
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Séminaire de géométrie arithmétique
In this talk, we will explain relation between u-power torsions in Breuil–Kisin prismatic cohomology and various pathologies in p-adic cohomology theories, as well as mention some new results. Part of the talk will be based on earlier joint works with Tong Liu, we shall also report some recent ongoing projects with Ofer Gabber and Alexander Petrov separately.
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
We show that Feynman integrals occurring in standard quantum field theories or perturbative worldline approaches to the scattering of  black holes are related to periods of Calabi-Yau varieties of various dimensions. After defining what mathematical properties a Calabi-Yau period motive has, we explain how the applications of the latter lead to an efficient analytic evaluation of the Feynman integrals in dimensional regularisation.
 
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The mapping class group of a surface is the group of isotopy classes of homeomorphisms of the surface. It acts on the space of conjugacy classes of morphisms from the fundamental group of the surface to some fixed Lie group. Such spaces are known as character varieties. In this talk we will investigate the rare phenomenon of finite orbits for mapping class group dynamics on character varieties. We will see how to construct non-trivial examples of finite orbits and give some intuition on how to classify all finite orbits when the target Lie group is SL(2,C). Most of this work is a collaboration with Samuel Bronstein.
 

When does a sequence of hyperbolic 3-manifolds with volume going to infinity have exponentially growing torsion homology? For arithmetic towers, the work of Bergeron-Sengun-Venkatesh suggests a set of conditions that conjecturally imply exponential growth of torsion homology. For nice sequences of hyperbolic 3-manifolds we use a different approach to find a condition implying exponential torsion homology growth: we give a condition on the spectrum of the Laplacian. I will give several motivations for this condition and show how to construct concrete examples of sequences satisfying it. This is based on joint work with Anshul Adve, Vikram Giri, Ben Lowe and Jonathan Zung.
 

Atttention : Les deux premières Leçons auront lieu à l’IMO, Amphithéâtre Yoccoz, le 16 mai à 10h et à 14h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
In Bernoulli bond percolation, we delete or retain each edge of a graph independently at random with some retention parameter p and study the geometry of the connected components (clusters) of the resulting subgraph. For lattices of dimension d>1, percolation has a phase transition, with a infinite cluster emerging at a critical probability pc(d). It is believed that critical percolation at and near the critical probability exhibits rich, fractal-like geometry that is expected to be approximately independent of the choice of lattice but highly dependent on the dimension d. In particular, various qualitative distinctions are expected between the low dimensional case d<6, the high-dimensional case d>6, and the critical case d=6, but this remains poorly understood particularly in dimensions d=3,4,5,6.In this course, I will give an overview of of what is known about critical percolation, focussing on recent advances in long-range and hierarchical models for which various aspects of intermediate-dimensional critical phenomena can now be understood rigorously.
 

Atttention : Les deux premières Leçons auront lieu à l’IMO, Amphithéâtre Yoccoz, le 16 mai à 10h et à 14h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
In Bernoulli bond percolation, we delete or retain each edge of a graph independently at random with some retention parameter p and study the geometry of the connected components (clusters) of the resulting subgraph. For lattices of dimension d>1, percolation has a phase transition, with a infinite cluster emerging at a critical probability pc(d). It is believed that critical percolation at and near the critical probability exhibits rich, fractal-like geometry that is expected to be approximately independent of the choice of lattice but highly dependent on the dimension d. In particular, various qualitative distinctions are expected between the low dimensional case d<6, the high-dimensional case d>6, and the critical case d=6, but this remains poorly understood particularly in dimensions d=3,4,5,6.In this course, I will give an overview of of what is known about critical percolation, focussing on recent advances in long-range and hierarchical models for which various aspects of intermediate-dimensional critical phenomena can now be understood rigorously.
 

Atttention : Les deux premières Leçons auront lieu à l’IMO, Amphithéâtre Yoccoz, le 16 mai à 10h et à 14h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
In Bernoulli bond percolation, we delete or retain each edge of a graph independently at random with some retention parameter p and study the geometry of the connected components (clusters) of the resulting subgraph. For lattices of dimension d>1, percolation has a phase transition, with a infinite cluster emerging at a critical probability pc(d). It is believed that critical percolation at and near the critical probability exhibits rich, fractal-like geometry that is expected to be approximately independent of the choice of lattice but highly dependent on the dimension d. In particular, various qualitative distinctions are expected between the low dimensional case d<6, the high-dimensional case d>6, and the critical case d=6, but this remains poorly understood particularly in dimensions d=3,4,5,6.In this course, I will give an overview of of what is known about critical percolation, focussing on recent advances in long-range and hierarchical models for which various aspects of intermediate-dimensional critical phenomena can now be understood rigorously.
 

Atttention : Les deux premières Leçons auront lieu à l’IMO, Amphithéâtre Yoccoz, le 16 mai à 10h et à 14h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
In Bernoulli bond percolation, we delete or retain each edge of a graph independently at random with some retention parameter p and study the geometry of the connected components (clusters) of the resulting subgraph. For lattices of dimension d>1, percolation has a phase transition, with a infinite cluster emerging at a critical probability pc(d). It is believed that critical percolation at and near the critical probability exhibits rich, fractal-like geometry that is expected to be approximately independent of the choice of lattice but highly dependent on the dimension d. In particular, various qualitative distinctions are expected between the low dimensional case d<6, the high-dimensional case d>6, and the critical case d=6, but this remains poorly understood particularly in dimensions d=3,4,5,6.In this course, I will give an overview of of what is known about critical percolation, focussing on recent advances in long-range and hierarchical models for which various aspects of intermediate-dimensional critical phenomena can now be understood rigorously.
 

New Structures and Techniques in p-adic Geometry        October 27-31, 2025 at IHES – Marilyn and James Simons Conference Center    How to get to IHES

In recent years, p-adic geometry has benefited from several new ideas. The goal of this conference is to invite experts to give lectures explaining some of these ideas and their uses.  The main themes are: motivic methods, categorical p-adic Langlands, and Igusa stacks.  Besides these mini-courses, there will also be some individual lectures by selected participants.
 Registration deadline: June 30, 2025
Speakers:

Johannes Anschütz (Université Paris-Saclay)
Ana Caraiani (Imperial College London)
Gabriel Dospinescu (CNRS, Université de Clermont-Auvergne)
Veronika Ertl (Université de Caen)
Eugen Hellmann (Universität Münster)
Kalyani Kansal (Imperial College London)
Dongryul Kim (Stanford University)
Arthur-César Le Bras (Université de Strasbourg)
Shubhodip Mondal (Purdue University)
Timo Richarz (TU Darmstadt)
Alberto Vezzani (Università degli Studi di Milano)
Mingjia Zhang (IAS, Princeton)

Organizing committee:     Dustin Clausen (IHES), Toby Gee (Imperial College London), Wiesława Nizioł (IMJ-PRG)
This conference is supported by the Simons Collaboration on Perfection in algebra, geometry, and topology