Dott. Davide A. Bignamini “Log-Sobolev inequalities and hypercontractivity for Ornstein-Uhlenbeck evolution operators in infinite dimensions”

The main focus of this talk will be on logarithmic Sobolev inequalities.
After a brief historical introduction to the topic, based on the works of E. Nelson and L. Gross, we will concentrate on the case of infinite-dimensional Ornstein-Uhlenbeck evolution operators. In particular, we will present hypercontractivity results, derived using suitable logarithmic Sobolev inequalities for the evolution system of measures associated with these
operators.