Fondation Mathématique Jacques Hadamard - FMJH

LMH

Labex mathématique Hadamard

Séminaire Itzykson

Date de dernière modification le 26 novembre 2018

Depuis novembre 2012, le labex LMH a mis en place un colloquium de Mathématiques et Physique intitulé "Séminaire Itzykson"coordonné par Nicolas Curien, Thibault Damour, Maxim Kontsevich, Kirone Mallick, Stéphane Nonnenmacher et Pierre Vanhove. Chaque session de ce séminaire a lieu  à l'IHES.

Ce colloquium dure une journée. Le matin est consacré à des exposés préparatoires visant à comprendre comment s'est mise en place la formulation mathématique du problème physique étudié ainsi qu'à donner un aperçu des enjeux et de l'histoire du sujet. L'après-midi est consacré à deux exposés, un donné par un mathématicien et l'autre par un physicien.

Parmi les thèmes déjà abordés : Chaos quantique, Cartes planaires et gravité quantique, Wall crossing in Hitchin integrable systems, Espaces de modules et courbes quantiques, Feynman Integrals, Physique statistique hors équilibre, Résurgence et quantification, Parafermionic observables and 2D statistical physics, Computational and information-theoretic phase transitions in large-scale inference problems. Les vidéos de certaines sessions sont visionnables sur les sites dailymotion et youtube.

Parmi les thèmes que nous comptons aborder dans le futur : la correspondance AdS-CFT, Cosmologie, Trous noirs,Théories de jauge et intégrabilité, méthodes de bootstrap en Théorie des champs conforme, Information quantique...

Le but de ce séminaire est de jeter les bases d'une véritable communauté scientifique autour des mathématiques et de la physique fondamentale dans la région de Saclay/Orsay/Bures, en particulier de faire partager aux mathématiciens les enjeux de la physique contemporaine. Le public visé est composé de mathématicien-nes et physicien-nes, incluant les étudiant-es en master ou doctorat ou en séjour postdoctoral.
La FMJH sera prête à considérer un soutien financier pour les frais de transports de jeunes chercheur-euses en dehors de la région parisienne.

 Retour à la page du programme math-physique.

9ème Séminaire Itzykson

Date de dernière modification le 26 novembre 2018

Le 9ème Séminaire Itzykson, portant sur le thème "Computational and information-theoretic phase transitions in large-scale inference problems" s'est tenu l'IHÉS (plan d'accès) le mercredi 21 novembre 2018.

Programme

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10h30-12h30 Laurent Massoulié (MSR-INRIA)

Minicourse

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14h-15h: Lenka Zdeborova (IPhT CEA)

Phase transition in regression and simple neural networks

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15h15-16h15: Andrea Montanari (Stanford)

Algorithms and computational phase transitions in low-rank estimation

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8ème Séminaire Itzykson

Date de dernière modification le 24 septembre 2018

Le 8ème Séminaire Itzykson, portant sur le thème "Parafermionic observables and 2D statistical physics" s'est tenu à l'IHÉS (plan d'accès) le Lundi 22 janvier 2018.

Programme

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10h-12h Hugo Duminil-Copin (IHES)

Introduction to parafermionic observables

In the early eighties, the physicists Belavin, Polyakov and Zamolodchikov postulated the conformal invariance of critical planar statistical models. This prediction enabled physicists to use Conformal Field Theory in order to formulate many conjectures on these models. From a mathematical perspective, proving rigorously the conformal invariance of a model (and properties following from it) constitutes a formidable challenge. In recent years, the connection between discrete holomorphicity and planar statistical physics led to spectacular progress in this direction. Kenyon, Chelkak and Smirnov exhibited discrete holomorphic observables in the dimer and Ising models and  roved their convergence to conformal maps in the scaling limit. These results paved the way to the rigorous proof of conformal invariance for these two models.

Other discrete observables have been proposed for a number of critical models, including self-avoiding walks and Potts models. While these observables are not exactly discrete holomorphic, their discrete contour integrals vanish, a property shared by discrete holomorphic functions. This property sheds a new light on the critical models, and we propose to discuss some of its applications. In particular, we will sketch the proof of a conjecture made by Nienhuis regarding the number of self-avoiding walks of length n on the hexagonal lattice.

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14h-15h: Denis Bernard (ENS Paris)

A (biased) semi-historical introduction to parafermionic fields in statistical physics

Starting from Kadanoff's and Ceva's construction, I will present an elementary introduction to different reincarnations of parafermionic observables and fields in statistical models and their relationships with braid group representations, quantum group  symmetries, integrability and holomorphicity.

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15h15-16h15: Dmitry Chelkak (ENS Paris & PDMI, St.Petersburg)

2D Ising fermions: from combinatorics to conformal invariance and s-embeddings

During the last decade, a number of results on conformal invariance of the critical 2D nearest-neighbor Ising model appeared, both for the small mesh size limits of correlation functions (fermions, energy densities, spins, disorders etc) and interfaces (aka domain walls) or loop ensembles arising in the model. We survey these results, which are based on discrete analysis techniques, notably on convergence theorems for solutions to some special boundary value problems for discrete holomorphic functions on rhombic lattices, and discuss the universality of the model with respect to an underlying planar graph.

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7e séminaire Itzykson : "Résurgence et quantification, Resurgence and Quantization"

Date de dernière modification le 29 mars 2017

Le 7ème Séminaire Itzykson, portant sur le thème "Résurgence et quantification" se tiendra à l'IHÉS (plan d'accès) le jeudi 20 avril 2017.

Formulaire d'inscription (l'inscription est gratuite mais nécessaire).

Les jeunes chercheurs venant de province peuvent demander un remboursement de leurs frais de transport au Labex Mathématique Hadamard (v. formulaire d'inscription).

Programme

10h - 12h
Marcos Mariño (Genève): Quantum theory and non-perturbative effects

13h30 - 14h30
Sergei Gukov (Caltech):  Resurgence and Modularity

14h45 - 15h45
Maxim Kontsevitch (IHES):  Semi-infinite topology of the complexified path integral.

16h - 17h
Ricardo Schiappa (Lisbonne & CERN): Resurgence Asymptotics in String Theory

Abstracts

Marcos Mariño (Genève): Quantum theory and non-perturbative effects

Abstract: Divergent series are ubiquitous in quantum theory, and one should learn to live with them and eventually make sense of them. A general framework to address these issues is the theory of resurgence by Ecalle. This requires the introduction of trans-series, or generalized formal series incorporating exponentially small effects, which are invisible in classical asymptotics. I will present the general framework of resurgence in down-to-earth terms, and discuss various examples in the theory of differential equations, Quantum Mechanics and in some (simple) Quantum Field Theories. In the last part of the talk I will summarize recent progress in the application of this program to topological string theory.

Sergei Gukov (Caltech):  Resurgence and Modularity

Abstract: Why do modular forms tend to have integer coefficients in their q-expansion? Are they counting something? And, can we "categorify" a modular form by representing it as a graded Euler characteristic of some homology theory? There are several ways to answer these questions, e.g. the one based on classical theory of modular forms relates them to counting points on elliptic curves and motives of higher-dimensional varieties. In this talk, we will ask these questions for mock modular forms, introduced by Ramanujan. They also exhibit q-expansion with integer coefficients and, surprisingly, the answer to these question is based on resurgent analysis of a different power series, which at first shows no signs of integrality!

Maxim Kontsevitch (IHES):  Semi-infinite topology of the complexified path integral.

Abstract: I will explain a viewpoint on resurgence via Floer-type topology of Lefschetz thimbles in the complexified path integral. In particular, so called 2d-4d wall-crossing formalism of Gaiotto, Moore and Neitzke arises naturally in this framework, without any reference to supersymmetric field theories.

Ricardo Schiappa (Lisbonne & CERN): Resurgence Asymptotics in String Theory

Following up on the morning lecture, I will give a very light introduction to resurgent asymptotics. These techniques will then be explored (again in the spirit of a light introduction) within transseries solutions of topological string theory, themselves obtained via a nonperturbative completion of the holomorphic anomaly equations.

Archives Séminaire Itzykson

Date de dernière modification le 20 février 2018
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