Matthias Meiwes (University of Tel Aviv, Israel) will speak in the geometry seminar on Tuesday 7 May, at 1.30pm in the Salle de Profs. Matthias’s title is Topological entropy and Hofer’s metric and his abstract is below.
A central object in the study of Hamiltonian diffeomorphisms on a symplectic manifold $(M,\omega)$ is Hofer’s metric, a bi-invariant metric on the group of Hamiltonian diffeomorphisms $\mathrm{Ham}(M,\omega)$ that displays rigidity and flexibility features that are special for those diffeomorphisms.
The geometry of this metric and its interplay with the dynamics has been thoroughly studied since its discovery by Hofer and his work in the early 90’s. In my talk, I will explain some ongoing work with Arnon Chor, in which we study stability properties of the topological entropy of Hamiltonian diffeomorphisms on closed surfaces $M$, and which leads to results on the genericity of positive entropy on $\mathrm{Ham}(M, \omega)$, formulated in terms of Hofer’s metric.
If time permits I will discuss possible generalizations of the results to higher dimensions.