Workshop Schlumberger :
Types dépendants et Formalisation des mathématiques

Le formalisme du lambda-calcul typé et des types dépendants fournit un système de notation non seulement pour les objets mathématiques (comme c’était le cas pour le formalisme utilisé par Bourbaki), mais également pour les preuves mathématiques. Ce formalisme est assez précis pour être représenté sur ordinateurs, et plusieurs systèmes interactifs de verification de preuves se fondent sur cette approche.

Ce sujet a connu ces 15 dernières  années des développements spectaculaires : des preuves non triviales ont ainsi été formalisées, comme celle du théorème des 4 couleurs, ou le théorème de Feit-Thompson, ou plus récemment, un lemme complexe de P. Scholze (liquid tensor experiment).

Dans une autre direction, un rapprochement inattendu entre ce formalisme et la notion de topos d’ordre supérieur a été mis en évidence.

Organisée par Thierry Coquand, titulaire de la chaire Schlumberger pour les sciences mathématiques à l’IHES, le but de ce cette journée est de faire le point sur ces développements récents, et d’explorer les limitations et possibilités de cette approche.

Conférenciers invités :

Benedikt Ahrens, Delft University of Technology
Anthony Bordg, University of Cambridge
Cyril Cohen, INRIA
Georges Gonthier, INRIA
Assia Mahboubi, INRIA
Patrick Massot, LMO, Université Paris-Saclay

The common knowledge is that mutations in genomes are caused by the mistakes of the Polymerase, the enzyme responsible for copying DNA (or RNA). However,  errors of polymerase must be symmetrical with respect to the change of the DNA or RNA strand. Surprisingly, mutations in the Human DNA Genome and in the RNA genome of the notorious SARS Cov2 virus are drastically asymmetric. We will discuss how this asymmetry of mutations helps to pinpoint the real cause of mutations in these genomes – chemical damage of DNA or RNA, and mechanisms whereby this damage actually causes mutations.

Connection to codes has emerged recently as a new tool to construct and study Narain CFTs with special properties. In the talk I will review this connection and argue that optimal theories, i.e. those maximizing the value of spectral gap for the given central charge, are code CFTs – meaning they can be constructed using codes. This applies to known optimal theories with c<=8 as well as to asymptotically large c. I will also discuss spinoff results, in particular construction of fake torus partition function Z(tau, bar tau), which satisfies all properties of the 2d CFT torus partition function (modular invariance, discreteness and positive-definiteness of spectrum), yet can be shown not to be a partition function of any 2d theory.

 

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We construct a cubic cut-and-join operator description for the partition functions of all semi-simple cohomological field theories, and, more generally, for the partition functions of the Chekhov-Eynard-Orantin topological recursion on a possibly irregular local spectral curve. The cut-and-join description leads to an algebraic version of topological recursion.
For the same partition functions, we also derive N families of the Virasoro constraints and prove that these constraints, supplemented by a deformed dimension constraint, imply the cut-and-join description.
The talk is based on arXiv:2202.09090.

Institut Des Hautes Etudes Scientifiques vous invite à une réunion Zoom planifiée.

Sujet : Séminaire de mathématique : M. Gromov
Heure : 17 mai 2022 10:00 AM Paris
        17 mai 2022 10:00 AM
        23 mai 2022 09:30 AM

Participer à la réunion Zoom
https://us02web.zoom.us/j/86379166463?pwd=WmRiNERvUEpUdGRYbitXZm5IWHdLZz09

ID de réunion : 863 7916 6463
Code secret : 644415

 

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

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 »
(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Institut Des Hautes Etudes Scientifiques vous invite à une réunion Zoom planifiée.

Sujet : Séminaire de mathématique : M. Gromov
Heure : 17 mai 2022 10:00 AM Paris
        17 mai 2022 10:00 AM
        23 mai 2022 09:30 AM

Participer à la réunion Zoom
https://us02web.zoom.us/j/86379166463?pwd=WmRiNERvUEpUdGRYbitXZm5IWHdLZz09

ID de réunion : 863 7916 6463
Code secret : 644415

 

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

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 »
(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Landau’s theory of Fermi liquids is a cornerstone of theoretical physics. I will show how to formulate Fermi liquid theory as an effective field theory of bosonic degrees of freedom, using the mathematical formalism of coadjoint orbits. While at the linear level, this theory reduces to existing multidimensional bosonization approaches, it necessarily features nonlinear corrections that are fixed by the geometry of the Fermi surface. These are crucial to reproduce nonlinear response, such as higher-point functions of currents. The effective field theory framework furthermore systematically parametrizes corrections to Fermi liquid behavior, and provides a computationally advantageous approach for non-Fermi liquids — strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions.

Participer à la réunion Zoom
https://us02web.zoom.us/j/87394591389?pwd=bFVaZHltckVaOXpZY1YrdWVVZUtHdz09

ID de réunion : 873 9459 1389
Code secret : 573006

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

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 quantum_encounters_seminar PRENOM NOM »
(indiquez vos propres prénom et nom) et laissez le corps du message vide.

In this talk I will describe constraints from causality and unitarity on 2→2 graviton scattering in weakly-coupled gravitational effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, I will explain how to derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Such bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis. In addition they demonstrate the gravity must be weakly coupled at all scales below Planck. Time permitting, I will comment on the experimental implications of the bounds.

Sujet : Quantum Encounter Seminar
Heure : 17 mai 2022 04:00 PM Paris

Participer à la réunion Zoom
https://us02web.zoom.us/j/85890403645?pwd=_WMK9e4w_JBbmNZFpTsnd4zUMmjnSa.1

ID de réunion : 858 9040 3645
Code secret : 301826

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

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 quantum_encounters_seminar PRENOM NOM »
(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Séminaire « Equations différentielles »

In Boltzmann’s billiard a particle moves in a half-plane subject to a central force and is reflected elastically when it hits the boundary. Boltzmann took the central force to be the sum of a gravitational inverse-square-law force and a centrifugal term proportional to the inverse cube of the distance to the centre. He formulated the expectation that except for special values of the parameters the system would be chaotic and would obey his Ergodic Hypothesis.  Recently Gallavotti and Jauslin showed that the system is integrable if the centrifugal term is omitted: it has a second conserved quantity besides the energy. I will review this result and show that this integrable Boltzmann system has the Poncelet property: if in a level set of the conserved quantities a trajectory is periodic then all trajectories on the level set are periodic. As for the classical Poncelet theorem on inscribed-circumscribed polygons in Jacobi’s interpretation, the result relies on the theory of elliptic curves. I will also present some work in progress with Michelle Wang on Boltzmann’s table tennis, the three dimensional version of Boltzmann’s integrable system, and the relation to QRT maps on biquadratic plane curves.

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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 « Equations différentielles »

The motivic Galois group is most naturally considered as an object in spectral algebraic geometry. However, deep conjectures in the theory of motives imply that the motivic Galois group is classical, i.e., has no higher derived information. We will discuss some recent attempts to verify the classicality of the motivic Galois group.

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

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.

A hyperbolic group acts on its Gromov boundary by homeomorphisms. In recent work with Jason Manning, we showed that for groups with sphere boundary, the boundary action is rigid in the sense of topological dynamics: any sufficiently small perturbation is semi-conjugate to the original action. In ongoing work also with Teddy Weisman, we are extending this result to all hyperbolic groups, using a coding argument in the spirit of Sullivan. This talk will introduce the rigidity problem and describe some of the tools towards the proof.

A group endowed with a probability measure comes naturally with a random walk. If moreover this group acts on some space, then one can push the random walk to the space under consideration, up to the choice of a basepoint. The resulting random walk is called the image random walk.

In this talk, motivated by numerous examples (hyperbolic groups acting on one of their Cayley graphs, mapping class groups acting on the corresponding curve complex…), the (discrete) groups will act on Gromov hyperbolic spaces. We will discuss the escape rate for such image random walks, and more precisely the associated large deviations problem.