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.
Marine Fontaine (University of Antwerp) will speak in the geometry seminar on Tuesday 10 December 2019 at 11am in the Salle de Profs. Marine’s title is Braids in the N-body problem by cabling a body in a central configuration and her abstract is below.
We prove the existence of periodic solutions of the N = n+1-body problem in an even dimensional Euclidean space: We start with n bodies whose reduced motion is close to a central configuration and we replace one of them by a pair of bodies rotating uniformly around their center of mass. When the motion takes place in the standard Euclidean plane these solutions are a special type of braid solutions. We use a variational formulation and the result is obtained by performing a Lyapunov-Schmidt reduction and the use of the Lyusternik-Schnirelmann category. This work is in collaboration with Carlos García-Azpeitia.