Séminaire « Equations différentielles »

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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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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 »
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Séminaire « Equations différentielles »

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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.

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

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 »
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Séminaire de géométrie arithmétique

I will report on a joint work with Klingler and Ullmo. Given a polarizable variation of Hodge structure on a smooth quasi projective variety S (e.g. the one associated to a family of pure motives over S), Cattani, Deligne and Kaplan proved that its Hodge locus (the locus of closed points of S where exceptional Hodge tensors appear) is a countable union of closed algebraic subvarieties of S. In this talk I will discuss when this Hodge locus is actually algebraic.

If time permits I will explain how a similar circle of ideas can be used to show the existence of a genus four curve of «Mumford’s type» (thus answering a question of Gross/Serre).

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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.

Séminaire de géométrie arithmétique

On considère le problème du calcul de la classe du champ classifiant BG d’un k-groupe G dans l’anneau de Grothendieck des champs $K_{0} ({rm Champs}_{k})$ défini par Ekedahl. Ce problème est lié à des questions d’arithmétique, de rationalité, à la cohomologie non-ramifiée et à la propriété de Tate mixte. On décrira nos résultats dans ce domaine.

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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.

Séminaire de géométrie arithmétique

I will give a report on my recent work on the arithmetic of rank 4 weight 3 Calabi-Yau motives. A conjectural relation between the derivatives of the L-functions of motives of analytic rank 1 and values of solutions to certain mixed Picard-Fuchs differential equations will be discussed.

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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.

Séminaire de géométrie arithmétique

Given a prime integer p, a non-archimedean local field F of residual characteristic p and a standard Borel subgroup P of ${GL}_{2} (F)$, Paškūnas proved that the restriction to P of (irreducible) smooth representations of ${GL}_{2} (F)$ over $overline{mathbb F}_p$ encodes a lot of information about the full representation of ${GL}_{2} (F)$ and that it leads to useful statement about p-adic representations of ${GL}_{2} (F)$. Nevertheless, the methods used at that time by Paškūnas heavily relied on the understanding of the action of certain spherical Hecke operator and on some combinatorics specific to the ${GL}_{2} (F)$ case. This method can be transposed case by case to for some other quasi-split groups of rank 1, but this is not very satisfying as such.

This talk will report on a joint work with J. Hauseux. Using Emerton’s ordinary parts functor, we get a more uniform context which shed a new light on Paškūnas’ results and allows us to generalize very naturally these results for arbitrary rank 1 groups. In particular, we prove that for such groups, the restriction of supersingular representations to a minimal parabolic subgroup is always irreducible.

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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 »
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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.

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

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 »
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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.

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

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.

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

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

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 »
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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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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 »
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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.

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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_physique PRENOM NOM »
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