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Accueil > Agenda scientifique

23 février 2021: 2 événements

  • Séminaire d’Analyse Fonctionnelle

    Mardi 23 février 13:45-15:00 - Michael Brannan - Texas A&M University

    Séminaire d’Analyse Fonctionnelle
    En savoir plus : Séminaire d’Analyse Fonctionnelle
  • Séminaire d’Analyse Fonctionnelle

    Mardi 23 février 16:00-17:00 - Michael Brannan - Texas A&M

    Complete logarithmic Sobolev inequalities and non-commutative Ricci curvature

    Résumé : I will give a brief introduction to the study of log-Sobolev type inequalities (LSI’s) for quantum Markov semigroups and some of their applications. In the context of classical heat semigroups on compact Riemannian manifolds, the famous Bakry-Emery theorem provides a beautiful connection between the geometry of the underlying manifold and the LSI, showing that a positive lower bound on the Ricci curvature implies an LSI for the heat semigroup. I will discuss an information-theoretic approach to obtain modified log-Sobolev inequalities based on non-positive non-commutative Ricci curvature lower bounds previously developed by Carlen and Maas. Using these tools, we are able to find new examples of quantum Markov semigroups satisfying a completely bounded version of the modified LSI, including heat semigroups on free quantum groups. This talk is based on joint work with Li Gao (TUM) and Marius Junge (UIUC).

    En savoir plus : Séminaire d’Analyse Fonctionnelle