Archives for November 2019

Sobhan Seyfaddini (Université Paris Diderot) will speak in the geometry seminar on Tuesday 26 November 2019 at 11h15am in the Salle de Profs. Sobhan’s title is Barcodes and Hamiltonian homeomorphisms and his abstract is below.

Hamiltonian homeomorphisms are those homeomorphisms of a symplectic manifold which can be written as uniform limits of Hamiltonian diffeomorphisms. One difficulty in studying Hamiltonian homeomorphisms (particularly in dimensions greater than two) has been that we possess fewer tools for studying them. For example, (filtered) Floer homology, which has been a very effective tool for studying Hamiltonian diffeomorphisms, is not well-defined for homeomorphisms. We will show in this talk that using barcodes and persistence homology one can indirectly define (filtered) Floer homology for Hamiltonian homeomorphisms. This talk is based on joint projects with Buhovsky-Humiliére and Le Roux-Viterbo.

Yakov Eliashberg (Stanford University) will speak in the geometry seminar on Thursday 2 April 2020 at 11am in the Salle de Profs. Yakov’s title and abstract are to be announced.

Hanne Van Den Bosch (Universidad de Chile, Santiago de Chile) will speak in the geometry seminar on Tuesday 17 December 2019 at 11am in the Salle de Profs. Hanne’s title is Dirac operators describing Graphene Quantum Dots and her abstract is below.

Low energy electronic excitations in graphene, a two-dimensional lattice of carbon atoms, are described effectively by a two–dimensional Dirac operator. For a bounded flake of graphene (a quantum dot), the choice of boundary conditions determines various properties of the spectrum. Several of these choices appear in the physics literature on graphene. For a simply connected flake and a family of boundary conditions, we obtain an explicit lower bound on the spectral gap around zero. We can also study the effect of the boundary conditions on eigenvalue sums in the semiclassical limit.
This is joint work with Rafael Benguria, Edgardo Stockmeyer (PUC, Chile), and Søren Fournais (Aarhus).

Cédric De Groote (Max Planck Institute, Leipzig) will speak in the geometry seminar on Tuesday 26 November 2019 at 10am in the Salle de Profs. Cédric’s title is Orderability up to conjugation of certain open contact manifolds and his abstract is below.

Eliashberg and Polterovich introduced in 2000 a notion of orderability for the group of contact isotopies of a contact manifold, which provides insights into the geometry of that group. Later, this same notion “up to conjugation” was used by Borman, Eliashberg and Murphy in their proof of the flexibility of overtwisted contact manifolds of all dimensions. I will review some of the history of that problem, and then present a new result on the orderability up to conjugation of certain contact annuli. This involves restating the problem as a contact non-squeezing result, which is then shown using a version of contact homology.