Przemyslaw Berk

Spectral disjointness of two dynamical systems is a very strong notion of absence of isomorphism. I will introduce basic definitions and provide a criterion for spectral disjointness of two automorphisms/flows. In the case of flows, I will apply this criterion to the study of linear time changes of Hamiltonian flows on the torus as well as two some classes of translation flows on surfaces of higher genera. In the case of automorphisms and certain classes of interval exchange transformations. I will illustrate our results, by sketching the proof of spectral disjointness of powers of interval exchange transformations. Finally, time permitting, I will mention ongoing projects related to the subject, in which I am involved. 
The talk is based on results obtained together with Adam Kanigowski.