Séminaire de géométrie arithmétique

Recently, it was realized that the local Langlands correspondence has a geometric and categorical formulation, with variants of such a formulation given independently by Emerton and Helm, Fargues and Scholze, Hellmann, and Zhu. All of these approaches essentially postulates an equivalence of categories, with one side being of automorphic flavor and the other side Galois. One advantage of such an approach is that it makes sense to consider more general representations on the automorphic side, which on the Galois side corresponds to coherent sheaves more general than skyscraper sheaves; some of these coherent sheaves are conjectured by Zhu to give cohomologies of Rapoport-Zink spaces in the local case and Shimura varieties in the global setup. In this talk I will formulate several conjectures attempting to match up explicitly objects under this equivalence of categories. First, I will give conjectural duals to the so-called degenerate Whittaker representations studied by Moeglin-Waldspurger: this conjecture is inspired by analogous conjectures of Gaiotto-Witten on S-duality of boundary conditions in supersymmetric Yang-Mills, and should be closely related to work of Ben-Zvi, Sakellaridis and Venkatesh. Secondly, starting on the Galois side, I will give conjectural duals to the coherent sheaves coming from the ramification filtration. I will then indicate how to prove various special cases of these conjectures.

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IHES Covid-19 regulations:

– all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
– speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
– Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

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The torus partition function of the critical O(n) model, which is known since 1987, does not fully characterize the space of states. For complex n, I will conjecture a determination of that space in terms of irreducible O(n) representations and indecomposable Virasoro representations. I will then describe the interplay between O(n) symmetry and crossing symmetry in four-point correlation functions, and explain how the solutions of crossing symmetry can be counted numerically. This leads to the determination of some of the model’s fusion rules.

This talk is based on the preprint https://arxiv.org/abs/2111.01106 with Linnea Grans-Samuelsson, Rongvoram Nivesvivat, Jesper Lykke Jacobsen, and Hubert Saleur.

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IHES Covid-19 regulations:

– all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
– speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
– Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

==================================================================

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 de géométrie arithmétique

Faltings’ approach in p-adic Hodge theory can be schematically divided into two main steps: firstly, a local reduction of the computation of the p-adic étale cohomology of a smooth variety over a p-adic local field to a Galois cohomology computation and then, the establishment of a link between the latter and differential forms. These relations are organized through Faltings ringed topos whose definition relies on the choice of an integral model of the variety, and whose good properties depend on the (logarithmic) smoothness of this model. Scholze’s generalization for rigid analytic varieties has the advantage of depending only on the variety (i.e. the generic fibre). Inspired by Deligne’s approach to classical Hodge theory for singular varieties, we establish a cohomological descent result for the structural sheaf of Faltings topos, which makes it possible to extend Faltings’ approach to any integral model, i.e. without any smoothness assumption. An essential ingredient of our proof is a descent result of perfectoid algebras in the arc-topology due to Bhatt and Scholze. 

As an application of our cohomological descent, using a variant of de Jong’s alteration theorem for morphisms of schemes due to Gabber-Illusie-Temkin, we generalize Faltings’ main p-adic comparison theorem to any proper and finitely presented morphism of coherent schemes over an absolute integral closure of Z_p (without any assumption of smoothness) for torsion étale sheaves (not necessarily finite locally constant). As a second application, we deduce a local version of the relative Hodge-Tate filtration from the global version constructed by Abbes-Gros.

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IHES Covid-19 regulations:

– all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
– speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
– Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

==================================================================

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  present a general construction in terms of Higgs bundles of the higher Teichmüller components of the character variety of a surface group for a real Lie group admitting a positive structure in the sense of Guichard-Wienhard. Key ingredients in this construction are the notion of magical sl2-triple, that we introduce, and the Cayley correspondence. Basics on Higgs bundle theory will be explained.
(Based on joint work with Bradlow, Collier, Gothen and Oliveira).

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IHES Covid-19 regulations:

– all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
– speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
– Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

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Two hyperbolic surfaces are said to be (length) isospectral if they have the same collection of lengths of primitive closed geodesics, counted with multiplicity (i.e. if they have the same length spectrum). For closed surfaces, there is an upper bound on the size of isospectral hyperbolic structures depending only on the topology. We will show that the situation is very different for infinite-type surfaces, by constructing large families of isospectral hyperbolic structures on surfaces of infinite genus.

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IHES Covid-19 regulations:

– all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
– speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
– Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

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In this seminar I will briefly review some success stories of Machine Learning applied to bio-medical domain up to date and speculate on what it will take to enable a much more substantial progress. I will specifically discuss Biology of Aging – the field which remains most promising and most fraudulent over the thousands of years in history of medical sciences. I will present my own work and suggest where theoretical approaches and modeling can make a big difference in a search for anti-aging and rejuvenating interventions.

More information:

 A recent interview with Longevity Technology on Radically Open Science platform

    https://www.longevity.technology/a-better-model-organism-for-testing-antiaging-drugs/

An interview with Llifespan.io on the state of aging science, Peshkin’s approaches and Machine Learning for Biology of Aging

     https://www.lifespan.io/news/an-interview-with-dr-leonid-peshkin/

   A 3 min video on Daphnia as a novel model organism for aging:

     https://vimeo.com/386647406

A preprint on Smart Tanks platform
     https://www.biorxiv.org/content/10.1101/2021.05.30.446339v1

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IHES Covid-19 regulations:

– all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
– speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
– Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

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The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods usually break one of the 3, which translates into the need to have an IR or UV cutoff. I will explain how a relativistic modification of continuous matrix product states allows us to satisfy the 3 requirements jointly in 1+1 dimensions. Optimizing over this class of states, one can solve scalar QFT without UV cutoff and directly in the thermodynamic limit, and numerics are promising. I will try to cover both the general philosophy of the method, the basics of the computations, and mention the many open problems.

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IHES Covid-19 regulations:

– all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
– speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
– Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

==================================================================

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

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IHES Covid-19 regulations:

– all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
– speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
– Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

==================================================================

Séminaire Laurent Schwartz — EDP et applications

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IHES Covid-19 regulations:

– all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
– speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
– Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

==================================================================

Séminaire Laurent Schwartz — EDP et applications

==================================================================

IHES Covid-19 regulations:

– all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
– speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
– Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

==================================================================

2022 IHES SUMMER SCHOOL

REMINDER: the participants of the Summer School who will come in person have been selected among a lot of applicants. Others, who were not selected but put on a waiting list won’t participate in person because the capacity of the conference center has been reached.

Therefore, if you are interested in participating but did not apply or haven’t been selected or invited to come, please register to participate through Zoom and don’t come to IHES. There are no more seats available and those who did apply and were selected through the application process have the priority to participate in person.

Thank you for your understanding and cooperation!

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Organizing Committee: Pierre-Henri Chaudouard (IMJ-PRG),  Wee Teck Gan (National Univ. of Singapore), Tasho Kaletha (Univ. of Michigan), Yiannis Sakellaridis (Johns Hopkins Univ.)

Scientific Committee: Gérard Laumon (Univ. Paris-Sud), Colette Mœglin (IMJ-PRG), Bảo Châu NGÔ (Chicago Univ.), Jean-Loup Waldspurger (IMJ-PRG)

The « Summer School on the Langlands Program » will be held at the Institut des Hautes Etudes Scientifiques (IHES) from 11 to 29 July. IHES is located in Bures-sur-Yvette, south of Paris (40 minutes by train from Paris).

This school is open to everybody but intended primarily for young participants, including Ph.D. students and postdoctoral fellows.

It has been almost 45 years since the influential summer school held in Corvallis, Oregon in 1977 brought together the leading experts of the Langlands program and defined the research agenda in this area for subsequent decades, at the same time inspiring and enabling several generations of young researchers to join in this exciting journey. This 3-week IHES summer school aims to do the same for the next phase of development in the Langlands program.

Recent decades have brought tremendous progress on the project of endoscopy, the extension of the Langlands program to the “relative” setting of spherical varieties and other related spaces, numerous successful “explicit” methods (such as the theta correspondence) to construct functoriality, novel ideas “beyond endoscopy”, and arithmetic applications of both the theta correspondence and the relative trace formula to the study of special cycles and their generating series. Ideas from the geometric Langlands program have begun impacting and enriching the classical Langlands program in significant ways. In particular, the idea that the “space of Langlands parameters” is not just a set, but a (putative) geometric space, can be used to organize a lot of developments around reciprocity, including the Taylor–Wiles method, derived structures, the Langlands correspondence over function fields, and the geometrization of the local Langlands conjecture.

The summer school will attempt to bring these exciting new directions together and explore their interactions.

SPEAKERS:

BEN-ZVI David (UT Austin)
BEUZART-PLESSIS Raphaël (Univ. Aix-Marseille)
CARAIANI Ana (Imperial College)
CHAUDOUARD Pierre-Henri (IMJ-PRG)
DAT Jean-François (IMJ-PRG)
EMERTON Matthew (Chicago Univ.)
FARGUES Laurent (IMJ-PRG)
FENG Tony (MIT)
FINTZEN Jessica (Duke Univ. & Cambridge Univ.)
GAN Wee Teck (National Univ. of Singapore)
GEE Toby (Imperial College)
HARRIS Michael (Columbia Univ.)
HELLMANN Eugen (Univ. Münster)
KALETHA Tasho (Univ. of Michigan)
LAPID Erez (Weizmann Inst.)
LI Chao (Columbia Univ.)
MASON-BROWN Lucas (Univ. of Oxford)
MOREL Sophie (ENS Lyon)
NGÔ Bảo Châu (Chicago Univ.)
PRASAD Dipendra (IIT Bombay)
RASKIN Sam (Univ. of Texas)
SAKELLARIDIS Yiannis (Johns Hopkins Univ.)
SCHOLZE Peter (Univ. Bonn)
SHIN Sug Woo  (UC Berkeley)
TAÏBI Olivier (ENS Lyon)
VENKATESH Akshay (IAS)
WEINSTEIN Jared (Boston Univ.)
XUE Cong (IMJ-PRG)
YUN Zhiwei (MIT)
ZHANG Wei (MIT)
ZHU Xinwen (CALTECH)
 

This is an IHES Summer School, organized in partnership with the Clay Mathematical Institute, the National Science Foundation, the support of the Société Générale, the FMJH and Qube RT.

 

A conference in honor of Thibault Damour

The conference will be held in a blended form, with talks given on site at IHES and others remotely through Zoom.

All the talks may be followed either online or on site (subject to availability).

Covid-19 regulations: for those who will attend in person, masks will be mandatory and we will ask them to provide a health pass upon their arrival.

Organized by Nathalie Deruelle (APC, Université de Paris), Alessandro Nagar (INFN Torino), and Slava Rychkov (IHES), the « Damour Fest: Adventures in Gravitation » will be held from October 12 to 15, 2021 at IHES.

 

Professor Thibault Damour is a permanent professor at IHES since 1989.
He is a theoretical physicist specializing in general relativity and string theory. He is known worldwide for his innovative work on black holes, gravitational waves, and quantum cosmology. Throughout his career, he has received numerous international awards, such as the prestigious Einstein Medal and the CNRS Gold Medal, and more recently (in 2021) the Galileo Galilei Medal, the ICTP Dirac medal, and the Balzan Prize. 

 

Invited speakers:

Leor Barack, University of Southampton
Sebastiano Bernuzzi, University of Jena
Lydia Bieri, Michigan University
Luc Blanchet, IAP, Paris
Alessandra Buonanno, AEI, MPI, Potsdam
Sophie De Buyl, Vrije Universiteit Brussel
Stanley Deser, Brandeis University
Marc Henneaux, Collège de France & ULB Bruxelles
Bala Iyer, ICTS, TIFR, Bangalore 
Piotr Jaranowski, University of Białystok
Sergiu Klainerman, Princeton University
Michael Kramer, MPI, Bonn
Juan Maldacena, IAS, Princeton
Viatcheslav Mukhanov, Ludwig Maximilian University, Munich
Hermann Nicolai, AEI, MPI, Potsdam
Adam Pound, University of Southampton
Giuseppe Policastro, ENS Paris
Alexander Polyakov, Princeton University
Manuel Rodrigues, ONERA, Université Paris-Saclay
Remo Ruffini, ICRA, Rome
David Shoemaker, MIT
Sergey Solodukhin, University of Tours
Alexei Starobinski, Landau Institute, Moscow
Gabriele Veneziano, CERN & Collège de France
Alex Vilenkin, Tufts University
Edward Witten, IAS, Princeton