Berlin-Hamburg-Seminar am 19.1.2024

Dustin Connery-Grigg (Jussieu) Spectral invariants and dynamics of low-dimensional Hamiltonian systems

Since their introduction by Schwarz in 2000 (following an earlier idea of Viterbo), spectral invariants have become a central tool in the modern Floer-theoretic study of Hamiltonian isotopies and diffeomorphisms. Unfortunately, given a particular Hamiltonian isotopy, it is often very difficult to compute its associated spectral invariants, and the relationship of these invariants to the underlying dynamics remains opaque. In this talk I will discuss a novel class of spectral invariants for Hamiltonian systems which share the main properties that make the classical spectral invariants useful, but which have the advantage of admitting a completely dynamical interpretation for generic Hamiltonian systems on surfaces.

Noémie Legout (Chalmers) Calabi-Yau structure on the Chekanov-Eliashberg algebra

We describe the Rabinowitz complex (a differential graded bimodule) associated to a pair of Legendrian submanifolds in a contact manifold. In the case where the pair of Legendrians is a 2-copy of a Legendrian sphere, we show that the acyclicity of the Rabinowitz complex is equivalent to the existence of an (n+1)-Calabi-Yau structure (in the sense of Ginzburg) on the Chekanov-Eliashberg algebra of the Legendrian sphere. This gives in particular an isomorphism between Hochschild homology and cohomology of the Chekanov-Eliashberg algebra, we extend on the chain level to a family of maps satisfying the A-infinity equations.