| Les deux révisions précédentes Révision précédente Prochaine révision | Révision précédente Prochaine révisionLes deux révisions suivantes |
| mega:seminaire [2019/02/05 15:22] – Titre et résumé Ségala male | mega:seminaire [2019/03/11 20:35] – [Prochaine séance] male |
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| ===== Prochaine séance ===== | ===== Prochaine séance ===== |
| * 10h30-12h00: mini cours par **[[https://www.math.u-psud.fr/~emaurel/|Édouard Maurel-Segala]]** // //\\ | * Vendredi **15 Mars** salle 421 |
| * 14h00-15h00: **[[https://sites.google.com/view/franck-gabriel-en/home|Franck Gabriel]]** ////\\ | * 10h30-12h00: mini cours par **[[https://www.di.ens.fr/~lelarge/|Marc Lelarge]]** //The cavity method for the spiked Wigner model.// We consider the high-dimensional inference problem where the signal is a low-rank symmetric matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension setting for the mutual information between the signal and the observations, as well as the matrix minimum mean squared error, while the rank of the signal remains constant. We unify and generalize a number of recent works on PCA, sparse PCA, submatrix localization or community detection by computing the information-theoretic limits for these problems in the high noise regime. \\ |
| * 15h00-16h30: **[[https://www.math.uni-sb.de/ag/speicher/weber.html|Moritz Weber]]** //Quantum symmetries of finite graphs and of noncommutative notions of independence//\\ | * 14h00-15h00: **[[http://math.univ-lyon1.fr/~lancien/|Cécilia Lancien]]** //Random correlation matrices: when are they with high probability classical or quantum?// Two observers performing binary outcome measurements on subsystems of a global system may obtain more strongly correlated results when they have a shared entangled quantum state than when they only have shared randomness. This well-known phenomenon of so-called Bell inequality violation can be precisely characterized mathematically. Indeed, being a classical or a quantum correlation matrix exactly corresponds to being in the unit ball of some tensor norms. In this talk, I will start with explaining all this in details. I will then look at the following problem: given a random matrix of size n, can one estimate the typical value of its "classical" and "quantum" norms, as n becomes large? For a wide class of random matrices, the answer is yes, and shows a separation between the two values. This result may be interpreted as follows: in a typical direction, the borders of the sets of classical and quantum correlations are separated away from each other. Based on joint work with Carlos Gonzalez-Guillen, Carlos Palazuelos and Ignacio Villanueva: "Random quantum correlations are generically non-classical", Ann. Henri Poincaré, 18(12):3793-3813 (2017).\\ |
| | * 15h30-16h30: **[[http://pub.ist.ac.at/~dschroed/|Dominik Schröder]]** //Cusp Universality for Wigner-type Random Matrices.// For Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner-Dyson-Mehta universality conjecture for the last remaining universality type.\\ |
| | |
| * Vendredi **8 Février, salle 201** | |
| * 10h30-12h00: mini cours par **[[https://www.math.u-psud.fr/~emaurel/|Édouard Maurel-Segala]]** //Étude de modèles de matrices par la méthode des cumulants libres.// Les cumulants libres sont un outil combinatoire qui permet de grandement simplifier la description des lois classiques en probabilités libres, qui apparaissent notamment lorsque l'on considère des limites de modèles matriciels de grande dimension. Ils permettent aussi de donner un critère pour vérifier la liberté de variables non-commutatives. Nous introduirons ces objets puis nous présenterons une manière de les calculer pour retrouver des résultats classiques de convergence de matrices aléatoires. Enfin nous montrerons comment on peut utiliser ces outils pour calculer des limites de spectres de matrices à noyaux, des modèles très utilisés en statistique et dont la limite est éclairée sous un jour très nouveau par l'étude de leurs cumulants libres.\\ | |
| * 14h00-15h00: **[[https://sites.google.com/view/franck-gabriel-en/home|Franck Gabriel]]** //Schur-Weyl-Jones duality and permutation-invariant random matrices.// Symmetries and independence of large random matrices induce an interesting asymptotic behavior: freeness in the unitary framework, traffic freeness in the symmetric framework. Using Schur-Weyl-Jones duality and defining a new order on partitions allows one to unify the two formalisms. In particular, this makes it possible to define cumulants for the theory of traffics and to generalize the notion of freeness for any easy orthogonal groups. We will use these results to study the asymptotic limit of matrix Lévy processes, such as unitary Brownian motion or random walks on the symmetric group: the limit of the latter defines a multiplicative traffic-free Lévy process which is not a free Lévy process. \\ | |
| * 15h30-16h30: **[[https://www.math.uni-sb.de/ag/speicher/weber.html|Moritz Weber]]** //Quantum symmetries of finite graphs and of noncommutative notions of independence.// In mathematics, symmetries are usually modeled by groups; in modern theories however, we sometimes need to go beyond groups in order to capture symmetry: We need quantum groups. In this talk, I will briefly motivate and introduce the concept of compact matrix quantum groups by Woronowicz from the 1980's based on C*-algebras. I will then focus on two aspects. Firstly, I will survey recent developments in the theory of quantum automorphism groups of graphs. This is a very young but promising field initiated by Bichon and Banica about fifteen years ago. Together with my PhD student Simon Schmidt, we showed that the quantum symmetry group of a graph C*-algebra is exactly the quantum automorphism group of the graph, hence the graph C*-algebra preserves the quantum symmetries of the underlying graph. A second focus of my talk will be on distributional symmetries for noncommutative independence concepts such as Voiculescu's free independence, Boolean independence or bi-free independence. For all these notions, we have a de Finetti type theorem characterizing iid sequences by distributional symmetries. The technical details of the talk will be mostly algebraic and no knowledge on C*-algebras or quantum groups is assumed.\\ | |
| ===== Calendrier 2018-2019 ===== | ===== Calendrier 2018-2019 ===== |
| * Vendredi **12 Octobre**, salle 201 | * Vendredi **12 Octobre**, salle 201 |
| * 15h30-16h30: **[[https://people.kth.se/~holcomb/|Diane Holcomb]]** //On the centered maximum of the Sine beta process//\\ | * 15h30-16h30: **[[https://people.kth.se/~holcomb/|Diane Holcomb]]** //On the centered maximum of the Sine beta process//\\ |
| * Vendredi **8 Février**, salle 201 | * Vendredi **8 Février**, salle 201 |
| * 10h30-12h00: mini cours par **[[https://www.math.u-psud.fr/~emaurel/|Édouard Maurel-Segala]]** // //\\ | * 10h30-12h00: mini cours par **[[https://www.math.u-psud.fr/~emaurel/|Édouard Maurel-Segala]]** //Étude de modèles de matrices par la méthode des cumulants libres//\\ |
| * 14h00-15h00: **[[https://sites.google.com/view/franck-gabriel-en/home|Franck Gabriel]]** //Schur-Weyl-Jones duality and permutation-invariant random matrices//\\ | * 14h00-15h00: **[[https://sites.google.com/view/franck-gabriel-en/home|Franck Gabriel]]** //Schur-Weyl-Jones duality and permutation-invariant random matrices//\\ |
| * 15h30-16h30: **[[https://www.math.uni-sb.de/ag/speicher/weber.html|Moritz Weber]]** //Quantum symmetries of finite graphs and of noncommutative notions of independence//\\ | * 15h30-16h30: **[[https://www.math.uni-sb.de/ag/speicher/weber.html|Moritz Weber]]** //Quantum symmetries of finite graphs and of noncommutative notions of independence//\\ |
| * Vendredi **15 Mars** salle 421 | * Vendredi **15 Mars** salle 421 |
| * mini cours par **[[https://www.di.ens.fr/~lelarge/|Marc Lelarge]]** ////\\ | * mini cours par **[[https://www.di.ens.fr/~lelarge/|Marc Lelarge]]** //The cavity method for the spiked Wigner model//\\ |
| * 14h00-15h00: **[[http://math.univ-lyon1.fr/~lancien/|Cécilia Lancien]]** ////\\ | * 14h00-15h00: **[[http://math.univ-lyon1.fr/~lancien/|Cécilia Lancien]]** //Random correlation matrices: when are they with high probability |
| * 15h30-14h30: **[[http://pub.ist.ac.at/~dschroed/|Dominik Schröder]]** ////\\ | classical or quantum?//\\ |
| | * 15h30-16h30: **[[http://pub.ist.ac.at/~dschroed/|Dominik Schröder]]** //Cusp Universality for Wigner-type Random Matrices//\\ |
| * pas de séance en **Avril** car Conférence du 15 au 19 à Luminy | * pas de séance en **Avril** car Conférence du 15 au 19 à Luminy |
| * Vendredi **10 Mai**, salle 314 | * Vendredi **10 Mai**, salle 314 |
| * 14h00-15h00: **[[https://davidgarciaz.wixsite.com/math|David Garcia Zelada]]** ////\\ | * 14h00-15h00: **[[https://davidgarciaz.wixsite.com/math|David Garcia Zelada]]** ////\\ |
| | * 15h30-16h30: **[[https://www-m7.ma.tum.de/bin/view/Analysis/SimoneWarzel|Simone Warzel]]** ////\\ |
| * Vendredi **14 Juin**, salle 201 | * Vendredi **14 Juin**, salle 201 |
| * 14h00-15h00: **[[https://cims.nyu.edu/~dubach/|Guillaume Dubach]]** ////\\ | * 14h00-15h00: **[[https://cims.nyu.edu/~dubach/|Guillaume Dubach]]** ////\\ |