11 octobre 2018

Olga Klopp (ESSEC et CREST)
Complétion de matrices à structure

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Lieu : salle 3L15

Résumé : Nous étudions les problèmes de l’estimation matricielle et de la complétion de matrice dans un cadre général. Le modèle général englobe plusieurs cas particuliers connus tels que le modèle de mélange gaussien, le modèle « mixed membership », le modèle « bi-clustering » et l’apprentissage de dictionnaires. Nous obtenons les vitesses de convergence optimales au sens minimax pour l’estimation de la matrice de signal en norme de Frobenius et en norme spectrale. Comme conséquence du résultat général, nous obtenons des taux de convergence minimax dans divers modèles particuliers.
C’est un travail en collaboration avec Yu Lu, Alexandre B. Tsybakov et Harrison H. Zhou.

Complétion de matrices à structure  Version PDF

S.V. Raghurama Rao (Department of Aerospace Engineering, Indian Institute of Science, Bangalore)
A Lattice Boltzmann Relaxation Scheme for Compressible Flows

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Lieu : IMO, Salle 3L8

Résumé : Traditional Lattice Boltzmann Method (LBM) is limited to incompressible flows, due to a built-in low Mach number expansion of the equilibrium distribution. A Lattice Boltzmann Relaxation Scheme for compressible flows is presented. The equilibrium distributions are simple functions of conserved variables and fluxes, avoiding low Mach number limitation. The results are presented for 1-D and 2-D Euler equations. New approaches are also introduced to approximate viscous Burgers equation.

A Lattice Boltzmann Relaxation Scheme for Compressible Flows  Version PDF

Valentina Franceschi (Orsay)
Essential self-adjointness of Sub-elliptic Laplacians

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Lieu : salle 2L8 (IMO, bâtiment 307)

Résumé : The aim of this seminar is to present recent results about essential self-adjointness of sub-elliptic laplacians. These are hypoelliptic operators defined on a manifold M, that are naturally associated to a geometric structure on it. In the case when such a structure is Riemannian and complete, the associated Laplace-Beltrami operator is indeed essentially self-adjoint. This amounts to say that the solutions to the Schrödinger equation on M are well defined without imposing any boundary conditions. Our purpose is to address the case when the structure is sub-Riemannian : this can be thought of as a generalization of the Riemannian case, under anisotropic constraints on the directions of motion on M. In particular, singularities may appear, encoded in the blow up of an intrinsic measure, whose definition depends only on the geometry. In this case the problem is still open and a standing conjecture, formulated by Boscain and Laurent, asserts that the sub-elliptic Laplacian is essentially self-adjoint. We will explain our results supporting the conjecture and underline the cases that are not included in our analysis. In collaboration with D. Prandi (CNRS, CentraleSupélec, Giffes-sur-Yvette, France) and L. Rizzi (CNRS & Institut Fourier, Grenoble, France)

Notes de dernières minutes : Café culturel assuré à 13h par Konstantin Pankrashkin

Essential self-adjointness of Sub-elliptic Laplacians  Version PDF

Vincent Vargas (ENS - DMA)
Some new estimates on Gaussian multiplicative chaos

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Lieu : 3L15

Résumé : Gaussian multiplicative chaos (GMC), introduced by Kahane in
1985, enables to define multifractal random measures formally defined by
the exponential of a log-correlated field. Recently, GMC has appeared in a
wide variety of contexts : Liouville gravity, Coulomb gases, the Riemann
zeta function, etc... In this talk, I will present recent elementary
estimates on GMC : tail expansions and small deviations. If time permits, I
will discuss applications of these results to the construction of a new
form of gravity predicted by string theorists which can be seen as the
quantum analogue of Kahler geometry.
Based on works with Lacoin and Rhodes.

Some new estimates on Gaussian multiplicative chaos  Version PDF