Institut de Mathématiques de Toulouse

Les événements de la journée


5 événements


  • Séminaire de Probabilités

    Mardi 13 mars 09:45-10:45 - Mathias Rousset - INRIA Rennes

    Theorème central limite pour les systèmes de particules de type Fleming-Viot, et application à la simulation d’évènements rares.

    Résumé : Dans cet exposé, on présentera un TCL pour un algorithme de simulation d’évènements rares appelé Adaptive Multilevel Splitting, qui duplique des particules en fonction d’un score afin de forcer la réalisation de scores élevés. La preuve est fondée sur la représentation de l’algorithme par un système de Fleming-Viot, et utilise le TCL pour les martingales cadlag.

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  • Séminaire de Statistique

    Mardi 13 mars 11:00-12:00 - Fabrice Gamboa - IMT

    Approximate Optimal Designs for Multivariate Polynomial Regression

    Résumé : We introduce a new approach aiming at computing approximate optimal designs for multivariate polynomial regressions on compact (semi-algebraic) design spaces. We use the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically the approximate optimal design problem. The geometry of the design is recovered via semidefinite programming duality theory. This work shows that the hierarchy converges to the approximate optimal design as the order of the hierarchy increases. Furthermore, we provide a dual certificate ensuring finite convergence of the hierarchy and showing that the approximate optimal design can be computed numerically with our method. As a byproduct, we revisit the equivalence theorem of the experimental design theory : it is linked to the Christoffel polynomial and it characterizes finite convergence of the moment-sum-of-square hierarchies.

    Lieu : Salle 106 1R1

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  • Séminaire de Géométrie et Topologie

    Mardi 13 mars 11:00-12:00 - Ehud Meir - Hambourg

    Hopf algebras via geometric invariant theory

    Résumé : Hopf algebras are an algebraic structure which appears in many areas of mathematics (such as representation theory, algebraic topology and operator algebras, to name a few).
    They can be considered as a generalization of a group to the non-commutative geometry setting.
    Their classification, however, even in group theoretical terms, is at present out of our reach.
    In this talk I will describe an alternative approach for studying Hopf algebras, by using tools from geometric invariant theory.
    By applying some classical results, I will show why the study of finite dimensional semisimple Hopf algebras can be reduced into studying some scalar invariants.
    I will then describe how these invariants relate to questions in Hopf algebra theory, and will describe an application to Hopf orders.
    If time permits, I will also describe other applications of geometric invariant theory in this direction.

    Lieu : Salle Pellos

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  • Séminaire MIP

    Mardi 13 mars 11:00-12:00 - Masahito Ohta - Tokyo University of Science

    Strong instability of standing waves for nonlinear Schrödinger equations with a partial confinement

    Résumé : We study the instability of standing wave solutions for nonlinear Schr\"odinger equations with a one-dimensional harmonic potential in dimension N greater than or equal to 2. We prove that if the nonlinearity is L^2-critical or supercritical in dimension N-1, then any ground-state standing waves are strongly unstable by blowup, that is,
    there exist finite time blowup solutions with initial data arbitrarily close to the standing waves. This shows that the upper bound of the nonlinearity in Bellazzini, Boussa\"id, Jeanjean and Visciglia (2017) is optimal for the existence of stable standing waves.

    Lieu : Salle MIP

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  • Homotopie en Géométrie Algébrique

    Mardi 13 mars 14:00-15:00 - B. Toën - IMT

    Espaces de modules de connexions

    Résumé : On présente un énoncé de représentabilité pour le problème de modules des connexions sur une variété non-nécessairement compacte. On tente de se convaincre que l’espace des modules correspondant est muni d’une structure de Poisson (avec décalage).

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