Przemysław Berk (Université Nicolas Copernic, Toruń) : Disjointness of rescalings of locally Hamiltonian flows

We show that for a typical locally Hamiltonian flow (T_t) on a surface, for any rational p, q such that |p| and |q| are distinct, the flows (T_pt) and (T_qt) are disjoint in the sense of Furstenberg. Our theorem works on surfaces of any genus, while previously known results were limited to a torus. I will introduce all the required definitions, present the background and sketch the proof which relies on finding the weak operator limits of so-called Koopman operators associated with the flow. 

The talk is based on a recent work with Corinna Ulcigrai.