| Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente Prochaine révisionLes deux révisions suivantes |
| mega:seminaire [2019/10/23 14:15] – Laure DUMAZ | mega:seminaire [2019/12/19 18:29] – [Prochaine séance] Guillaume BARRAQUAND |
|---|
| * **Calendrier.** https://calendar.google.com/calendar/ical/qn5qq7dlmp38sc624s4png8umc%40group.calendar.google.com/public/basic.ics | * **Calendrier.** https://calendar.google.com/calendar/ical/qn5qq7dlmp38sc624s4png8umc%40group.calendar.google.com/public/basic.ics |
| ===== Prochaine séance ===== | ===== Prochaine séance ===== |
| * Vendredi **8 novembre**, salle 421 le matin, 314 l'après-midi | * Vendredi **17 janvier**, salle 201 |
| * 10h30-12h00: **[[http://www.phys.ens.fr/~barraquand/|Guillaume Barraquand]]**// Kardar-Parisi-Zhang universality class: old and new.// The KPZ universality class is a set of diverse statistical mechanics models which can be described by an evolving interface and are conjectured to share the same non-Gaussian large scale behaviour. This class includes interacting particle systems, growth models, directed polymers in random media, and stochastic PDEs such as the KPZ equation. The first part of the talk will be an introduction to this subject where we will emphasize connections to the study of random matrices. In the second part of the talk, we will review (superficially) some recent advances about the definition of the so-called KPZ fixed point, that is the universal space time random field which all models in the KPZ class conjecturally converge to.\\ | * 10h30-12h00: **[[https://webusers.imj-prg.fr/~frederic.klopp/|Frédéric Klopp]]**////\\ |
| * 14h00-15h00: **[[http://www.i2m.univ-amu.fr/perso/charles.bordenave/start|Charles Bordenave]]** //Liberté asymptotique forte pour des représentations de matrices unitaires aléatoires indépendantes. //Travail en collaboration avec Benoit Collins. On prend une représentation unitaire de U(n) de dimension n^q obtenue en prenant q produits tensoriels d'une matrice unitaire ou de sa conjuguée. On considère des matrices indépendantes distribuées suivant la mesure de Haar sur U(n) ou O(n) et on démontre que leurs représentations sont fortement asymptotiquement libres dans l'orthogonal d'un espace vectoriel de petite dimension. Pour le cas le plus simple q = 1 de la représentation fondamentale, on retrouve un résultat de Collins et Male avec un argument complètement différent. La preuve est basée sur les opérateurs sans épines, le calcul de Weingarten et la méthode des grandes traces. \\ | * 14h00-15h00: **[[https://www.lpthe.jussieu.fr/~zuber/|Jean-Bernard Zuber]]**// A review of Horn's problem //\\ |
| * 15h30-16h30: ** [[https://www2.math.binghamton.edu/p/people/renfrew/start|David Renfrew]] ** //Randomly coupled differential equations and non-Hermitian random matrices. //We consider large random matrices, whose entries can contain non-trivial correlations and possibly different variances, and compute the limiting support of their eigenvalues, as well as the trace of f(X)g(X*) for analytic test functions f and g. We then consider applications to long time asymptotics for systems of critically coupled differential equations with random coefficients.\\ | Horn's problem deals with the following question: what can be said about the spectrum of eigenvalues of the sum C=A+B of two Hermitian matrices of given spectrum ? The support of the spectrum of C is now well understood, after a long series of works from Weyl (1912) to Horn (1952) to Klyachko (1998) and Knutson and Tao (1999). The problem has also amazing connections with group theory and the decomposition of tensor product of representations. \\ \\ Comparison with the same problem for real symmetric matrices and the action of the orthogonal group reveals similarities but also unexpected differences... \\ \\ In this talk, after a short introduction to the problem, I’ll sketch the computation of the probability distribution function of the eigenvalues of C, when A and B are independently and uniformly distributed on their orbit under the action of the group.\\ |
| | \\ If time permits, I'll also review some aspects of the connection with representation theory. |
| | |
| | * 15h30-16h30: **[[http://perso.ens-lyon.fr/adrien.kassel/|Adrien Kassel]]**////\\ |
| |
| ===== Calendrier 2019-2020 ===== | ===== Calendrier 2019-2020 ===== |
| * Vendredi **6 décembre**, séance annulée | * Vendredi **6 décembre**, séance annulée |
| * Vendredi **17 janvier**, salle 201 | * Vendredi **17 janvier**, salle 201 |
| * 10h30-12h00: ////\\ | * 10h30-12h00: **[[https://webusers.imj-prg.fr/~frederic.klopp/|Frédéric Klopp]]**////\\ |
| * 14h00-15h00: **[[https://www.lpthe.jussieu.fr/~zuber/|Jean-Bernard Zuber]]**////\\ | * 14h00-15h00: **[[https://www.lpthe.jussieu.fr/~zuber/|Jean-Bernard Zuber]]**////\\ |
| * 15h30-16h30: **[[http://perso.ens-lyon.fr/adrien.kassel/|Adrien Kassel]]**////\\ | * 15h30-16h30: **[[http://perso.ens-lyon.fr/adrien.kassel/|Adrien Kassel]]**////\\ |
| * Vendredi **7 février**, salle 421 le matin, amphi Hermite l'après-midi | * Vendredi **7 février**, salle 421 le matin, amphi Hermite l'après-midi |
| * 10h30-12h00: ////\\ | * 10h30-12h00: **[[http://djalil.chafai.net/|Djalil Chafaï]]**////\\ |
| * 14h00-15h00: ////\\ | * 14h00-15h00: ////\\ |
| * 15h30-16h30: ////\\ | * 15h30-16h30: ////\\ |
| * 14h00-15h00: ////\\ | * 14h00-15h00: ////\\ |
| * 15h30-16h30: ////\\ | * 15h30-16h30: ////\\ |
| * Vendredi **15 mai**, salle 314 l'après-midi | * Vendredi **7 mai**, salle 201 |
| * 10h30-12h00: ////\\ | * 10h30-12h00: ////\\ |
| * 14h00-15h00: ////\\ | * 14h00-15h00: ////\\ |