Melchior Wirth (IST Austria)

Markov semigroups are semigroups of operators on certain function spaces that preserve positivity and the constant functions. The noncommutative analogue of Markov semigroups are quantum Markov semigroups, which act on spaces of operators instead of function spaces. From the very beginning when they were introduced in the study of open quantum systems, a central topic of research on quantum Markov semigroups has focused on describing their generators. In this talk I will report on recent progress concerning the structure of these generators for semigroups that satisfy a certain symmetry condition, called GNS symmetry. I will give applications to the problem of extending GNS-symmetric quantum Markov semigroups and the characterization of hypercontractivity in terms of logarithmic Sobolev inequalities.
_{Contact: Marcel Schmidt}