Felix Schlenk (Université de Neuchâtel, Switzerland) will speak in the geometry seminar on Tuesday 11 June, at 11.30am in the Salle de Profs. Felix’s title and abstract are to be announced.

Matthias’s title is Manning’s inequality for Finsler and Reeb flows and his abstract is below.

I will explain parts of recent work with Marcelo Alves and Alberto Abbondandolo, in which we study entropy rigidity for Reeb flows and Finsler flows. An important result in the study of the topological entropy for geodesic flows is Manning’s inequality, that bounds the topological entropy from below by the volume entropy.
I will discuss two ways to extend this result to Finsler and Reeb flows.

Claude LeBrun (Stony Brook University) will speak in the geometry seminar on Wednesday 26 of June. Claude’s title is Einstein Metrics, Harmonic Forms, and Conformally Kähler Geometry and his abstract is below.

There are certain compact 4-manifolds, such as real and complex hyperbolic 4-manifolds, 4-tori, and K3, where we completely understand the moduli space of Einstein metrics. But there are vast numbers of other 4-manifolds where we know that Einstein metrics exist, but cannot currently determine whether or not there are other Einstein metrics on them that are qualitatively different from the currently-known ones. In this lecture, I will first present a characterization of the known Einstein metrics on Del Pezzo surfaces that I discovered several years ago, and then describe a delicate generalization which I obtained only quite recently.

Angela Pasquale (Université de Lorraine) will speak in the geometry seminar on Monday 1st of April, at 2pm in the Salle de Profs. Angela’s title is Resonances of the Laplacian on products of rank-one symmetric spaces and her abstract is below. [Read more…]

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.