Séminaire « Equations différentielles »

A new seminar «Differential Equations»  will start at the IHES.

Seminar Program:

A short address (V. Roubtsov)

Talk «From quantum cohomology for grassmannians to motivic Gamma-functions» (V. Golyshev)

The talk will followed by an organizational discussion.

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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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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.

Surface group representations inside PU(2,1) share some geometric properties with Kleinian groups but also with real projective representations, related to divisible convex sets.
A central object for understanding their properties is the limit sets in the sphere at infinity. I will present computer generated figures of these limit sets that help build some intuition for deformations of real Fuchsian representations. This leads to a new tool for working with these deformations, which we call thinness.
Joint work (in progress) with E. Falbel and P. Will.

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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 70 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 70 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 free Burnside group B(r,n) is the quotient of the free group of rank r by the normal subgroup generated by the n-th power of all its elements. It was introduced in 1902 by Burnside, who asked whether B(r,n) is necessarily a finite group or not. In 1968 Novikov and Adian proved that if r > 1 and n is a sufficiently large odd exponent, then B(r,n) is actually infinite. It turns out that B(r,n) has a very rich structure. In this talk we are interested in understanding equations in B(r,n). In particular we want to investigate the following problem: given a set of equations S, under which conditions does every solution to S in B(r,n) already come from a solution in the free group of rank r?
Along the way we will explore other aspects of certain periodic groups (i.e. quotients of a free Burnside group) such as the Hopf / co-Hopf property, the isomorphism problem, their automorphism groups, etc.
Joint work with Z. Sela.

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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 70 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 70 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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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

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.

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

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.

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.

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