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…]

# Archives for February 2019

## Matthias Meiwes to speak in the geometry seminar, Tuesday 7 May

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.

## Alessandra Pluda to speak in the geometry seminar, 30 April

Alessandra Pluda (Universitat Regensburg) will speak in the geometry seminar on Tuesday 30 April, at 1.30pm in the Salle de Profs. Alessandra’s title is *Motion by curvature of networks: analysis of singularities and “restarting” theorems* and her abstract is below.

A regular network is a finite union of sufficiently smooth curves whose end points meet in triple junctions. We will present the state-of-the-art of the problem of the motion by curvature of a regular network of curves in the plane mainly focusing on singularity formation. Then we will discuss the need of a “restarting” theorem for networks with multiple junctions of order bigger than three and we will give an idea of a possible strategy to prove it. These results are in collaboration with Rafe Mazzeo (Stanford University), Mariel Saez (P. Universidad Catolica de Chile) and Jorge Lira (University of Fortaleza).