Cari colleghi, vi annuncio che martedì 8 novembre, alle ore 15 precise, nell'aula Beltrami del Dipartimento di Matematica dell'Universita' di Pavia, il Dott. Cambyse Rouzé (University of Cambridge) terrà un seminario dal titolo Convergence properties of a quantum diff usion semigroup via concavity of the quantum entropy power di cui segue il sunto. Distinti saluti, Raffaella Carbone Abstract The entropy power, rst de ned by Shannon in his seminal paper, lead to many celebrated results in information theory and probability theory. In 1985, Costa proved that the entropy power of a random variable with added Gaussian noise of linearly increasing variance is concave with respect to . The proof of this result was later simpli ed by Dembo by an argument based on the so-called Blachman-Stam inequality. This result (and the intermediate steps of its proof) led to many applications ranging from contractivity properties of certain Markov semigroups to entropic versions of the Central limit theorem. In this talk I will discuss a recent analogue of this result proved in the context of quantum harmonic analysis on phase space. I will then use this result to bound the time of convergence in relative entropy of a state evolving under a quantum analogue of the heat semigroup. This is joint work with Dr. Nilanjana Datta and Dr. Yan Pautrat. -- Raffaella Carbone, PhD Ricercatore di Probabilità e Statistica Matematica Dipartimento di Matematica dell'Università degli Studi di Pavia