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23 février 2021: 2 événements
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Séminaire d’Analyse Fonctionnelle
En savoir plus : Séminaire d’Analyse FonctionnelleMardi 23 février 13:45-15:00 - Michael Brannan - Texas A&M University Séminaire d’Analyse Fonctionnelle -
Séminaire d’Analyse Fonctionnelle
En savoir plus : Séminaire d’Analyse FonctionnelleMardi 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).