Berlin-Hamburg-Seminar am 10.12.2018

Vincent Humiliere (Paris)  C⁰ continuity of bar codes

Lev Buhovsky, Sobhan Seyfaddini and I recently proved that the Hamiltonian spectral norm behaves continuously with respect to C⁰ topology on the space of Hamiltonian diffeomorphisms on symplectically aspherical manifolds. Using a result of Kislev and Shelukhin, this implies the C⁰-continuity of the "bar-codes" defined from Floer homology. My plan is to introduce these objects, give an idea of the proofs and provide some applications.

Luis Diogo (Uppsala)  Knot contact homology and the Alexander polynomial

Knot contact homology is an invariant of knots in 3-dimensional space. It carries a lot of information about the knot, and in particular it specifies a 3-dimensional polynomial, called the augmentation polynomial of the knot. We will discuss a formula relating the augmentation polynomial and the Alexander polynomial of the knot. The proof involves the study of moduli spaces of pseudoholomorphic curves (annuli and strips) in the cotangent bundle of the 3-sphere, with boundary components mapping to the zero section and to a Lagrangian diffeomorphic to the knot complement. This is joint work with Tobias Ekholm.