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 (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).

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Stéphane Launois (University of Kent) will speak in the geometry seminar on Tuesday 12 March, at 1.30pm in the Salle de Profs. Stéphane’s title and abstract are to be announced.

Mariel Saez (Pontificia Universidad Catolica, Chile) will speak in the geometry seminar on Tuesday 26 February, at 2pm in the Salle de Profs. Mariel’s title is On the uniqueness of graphical mean curvature flow and her abstract is below. [Read more…]