Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019-2021 jointly with A. Kaviraj and E. Trevisani and published in [1-4], which aims to explain these facts.

Outline:
1. Random Field Ising Model: phase diagram, well-established facts and experiments.
2. Numerical results for the dimensional reduction of critical exponents: “no” for d=3,4, “yes” for d=5.
3. Parisi-Sourlas supersymmetry implies dimensional reduction
4. Generalities about RG fixed point disappearance
5. Loss of Parisi-Sourlas SUSY via dangerously irrelevant operators?
6. Replica field theory. Cardy field transform “derivation » of Parisi-Sourlas SUSY and its potential loopholes.
7. Replica symmetric interactions in the Cardy basis
8. Leader and follower interactions
9. Classification of leaders
10. Anomalous dimension computations and results. Evidence for the SUSY fixed point instability below ~4.5
11. Future directions and open problems.

Literature:
[1] A. Kaviraj, S. Rychkov, E. Trevisani, « Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT, » [arXiv:1912.01617] JHEP 2004 (2020) 090
[2] A. Kaviraj, S. Rychkov, E. Trevisani, « Random Field Ising Model and Parisi-Sourlas Supersymmetry II. Renormalization Group”, [arXiv:2009.10087] JHEP 03 (2021) 219
[3] A. Kaviraj, S. Rychkov, E. Trevisani, « The fate of Parisi-Sourlas supersymmetry in Random Field models”, [arXiv:2112.06942] Phys.Rev.Lett. 129 (2022) 045701
[4] A. Kaviraj, E. Trevisani, « Random Field φ^3 Model and Parisi-Sourlas Supersymmetry », [arXiv:2203.12629] JHEP 08 (2022) 290

Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019-2021 jointly with A. Kaviraj and E. Trevisani and published in [1-4], which aims to explain these facts.

Outline:
1. Random Field Ising Model: phase diagram, well-established facts and experiments.
2. Numerical results for the dimensional reduction of critical exponents: “no” for d=3,4, “yes” for d=5.
3. Parisi-Sourlas supersymmetry implies dimensional reduction
4. Generalities about RG fixed point disappearance
5. Loss of Parisi-Sourlas SUSY via dangerously irrelevant operators?
6. Replica field theory. Cardy field transform “derivation » of Parisi-Sourlas SUSY and its potential loopholes.
7. Replica symmetric interactions in the Cardy basis
8. Leader and follower interactions
9. Classification of leaders
10. Anomalous dimension computations and results. Evidence for the SUSY fixed point instability below ~4.5
11. Future directions and open problems.

Literature:
[1] A. Kaviraj, S. Rychkov, E. Trevisani, « Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT, » [arXiv:1912.01617] JHEP 2004 (2020) 090
[2] A. Kaviraj, S. Rychkov, E. Trevisani, « Random Field Ising Model and Parisi-Sourlas Supersymmetry II. Renormalization Group”, [arXiv:2009.10087] JHEP 03 (2021) 219
[3] A. Kaviraj, S. Rychkov, E. Trevisani, « The fate of Parisi-Sourlas supersymmetry in Random Field models”, [arXiv:2112.06942] Phys.Rev.Lett. 129 (2022) 045701
[4] A. Kaviraj, E. Trevisani, « Random Field φ^3 Model and Parisi-Sourlas Supersymmetry », [arXiv:2203.12629] JHEP 08 (2022) 290

Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019-2021 jointly with A. Kaviraj and E. Trevisani and published in [1-4], which aims to explain these facts.

Outline:
1. Random Field Ising Model: phase diagram, well-established facts and experiments.
2. Numerical results for the dimensional reduction of critical exponents: “no” for d=3,4, “yes” for d=5.
3. Parisi-Sourlas supersymmetry implies dimensional reduction
4. Generalities about RG fixed point disappearance
5. Loss of Parisi-Sourlas SUSY via dangerously irrelevant operators?
6. Replica field theory. Cardy field transform “derivation » of Parisi-Sourlas SUSY and its potential loopholes.
7. Replica symmetric interactions in the Cardy basis
8. Leader and follower interactions
9. Classification of leaders
10. Anomalous dimension computations and results. Evidence for the SUSY fixed point instability below ~4.5
11. Future directions and open problems.

Literature:
[1] A. Kaviraj, S. Rychkov, E. Trevisani, « Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT, » [arXiv:1912.01617] JHEP 2004 (2020) 090
[2] A. Kaviraj, S. Rychkov, E. Trevisani, « Random Field Ising Model and Parisi-Sourlas Supersymmetry II. Renormalization Group”, [arXiv:2009.10087] JHEP 03 (2021) 219
[3] A. Kaviraj, S. Rychkov, E. Trevisani, « The fate of Parisi-Sourlas supersymmetry in Random Field models”, [arXiv:2112.06942] Phys.Rev.Lett. 129 (2022) 045701
[4] A. Kaviraj, E. Trevisani, « Random Field φ^3 Model and Parisi-Sourlas Supersymmetry », [arXiv:2203.12629] JHEP 08 (2022) 290

Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any d. I will present a recent theory, developed in 2019-2021 jointly with A. Kaviraj and E. Trevisani and published in [1-4], which aims to explain these facts.

Outline:
1. Random Field Ising Model: phase diagram, well-established facts and experiments.
2. Numerical results for the dimensional reduction of critical exponents: “no” for d=3,4, “yes” for d=5.
3. Parisi-Sourlas supersymmetry implies dimensional reduction
4. Generalities about RG fixed point disappearance
5. Loss of Parisi-Sourlas SUSY via dangerously irrelevant operators?
6. Replica field theory. Cardy field transform “derivation » of Parisi-Sourlas SUSY and its potential loopholes.
7. Replica symmetric interactions in the Cardy basis
8. Leader and follower interactions
9. Classification of leaders
10. Anomalous dimension computations and results. Evidence for the SUSY fixed point instability below ~4.5
11. Future directions and open problems.

Literature:
[1] A. Kaviraj, S. Rychkov, E. Trevisani, « Random Field Ising Model and Parisi-Sourlas Supersymmetry I. Supersymmetric CFT, » [arXiv:1912.01617] JHEP 2004 (2020) 090
[2] A. Kaviraj, S. Rychkov, E. Trevisani, « Random Field Ising Model and Parisi-Sourlas Supersymmetry II. Renormalization Group”, [arXiv:2009.10087] JHEP 03 (2021) 219
[3] A. Kaviraj, S. Rychkov, E. Trevisani, « The fate of Parisi-Sourlas supersymmetry in Random Field models”, [arXiv:2112.06942] Phys.Rev.Lett. 129 (2022) 045701
[4] A. Kaviraj, E. Trevisani, « Random Field φ^3 Model and Parisi-Sourlas Supersymmetry », [arXiv:2203.12629] JHEP 08 (2022) 290

Let G be a finitely generated group acting faithfully by linear transformations on a finite-dimensional complex vector space. The theorems of Malcev, Selberg, or Tits provide important properties satisfied by G. To what extent do these properties continue to hold when G is acting by polynomial (instead of linear) transformations? In order to address this question, I shall describe a few results that illustrate how one can use p-adic or finite fields for problems which are initially phrased in terms of complex numbers. 

Let Xk,d denote the space of rank-k lattices in Rd. Topological and statistical properties of the dynamics of discrete subgroups of G=SL(d,R) on Xd,d were described in the seminal works of Benoist-Quint. A key step/result in this study is the classification of stationary measures on Xd,d. Later, Sargent-Shapira initiated the study of dynamics on the spaces Xk,d. When k ≠ d, the space Xk,d is of a different nature and a clear description of dynamics on these spaces is far from being established. Given a probability measure μ which is Zariski-dense in a copy of SL(2,R) in G, we give a classification of μ-stationary measures on Xk,d and prove corresponding equidistribution results. In contrast to the results of Benoist-Quint, the type of stationary measures that μ admits depends strongly on the position of SL(2,R) relative to parabolic subgroups of G. I will start by reviewing preceding major works and ideas. The talk will be accessible to a broad audience. Joint work with Alexander Gorodnik and Jialun Li. 

We approximate boundaries of convex polytopes  by smooth hypersurfaces with positive mean curvatures and, by using basic geometric relations between the scalar curvatures of Riemannian manifolds and the mean curvatures of their boundaries, establish lower bound on the dihedral angles of these polytopes.

Port du masque obligatoire / Mask mandatory

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

Sujet : Séminaire de mathématique : M. Gromov
Heure : 27 juin 2022 02:00 PM Paris

Participer à la réunion Zoom
https://us02web.zoom.us/j/87455718639?pwd=oDF-dSYQd8Sevw2yEd1AVx4-HzxrBF.1

ID de réunion : 874 5571 8639
Code secret : 052856

 

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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LSC, which stands for Life, Structure, and Cognition, is an initiative with the aim of learning about the latest advancements and of exploring the modalities for cooperative progress between Biology and Artificial Intelligence, as is already starting to take place under our eyes. The goal is to investigate how biological systems evolved cognitive functions, using AI both as a concept toolbox and as a tool, and in turn, investigate how biological systems can serve as models to understand and stimulate new progress in AI.

The idea of LSC is an annual evaluation, expert discussion, and lecture series on the key topics and latest advancements in these directions, thus the Life and Cognition components of LSC. Structure in this LSC epithet refers to Mathematics and how it might and must help process and formalize aspects of these advancements. 

LSC 2022 Webinars

LSC 2022 Meeting

ORGANIZING COMMITTEE:

– Yves Barral (ETH Zürich)
– Mikhail Gromov (IHES, Université Paris-Saclay)
– Robert Penner (IHES, Université Paris-Saclay)
– Vasily Pestun (IHES, Université Paris-Saclay)

Stay in touch, subscribe to our mailing list.

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.

 

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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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.