BerlinHamburgSeminar am 19.1.2024
Dustin ConneryGrigg (Jussieu) Spectral invariants and dynamics of lowdimensional 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 Floertheoretic 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) CalabiYau structure on the ChekanovEliashberg 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 2copy of a
Legendrian sphere, we show that the acyclicity of the Rabinowitz
complex is equivalent to the existence of an (n+1)CalabiYau structure
(in the sense of Ginzburg) on the ChekanovEliashberg algebra of the
Legendrian sphere. This gives in particular an isomorphism between
Hochschild homology and cohomology of the ChekanovEliashberg algebra,
we extend on the chain level to a family of maps satisfying the
Ainfinity equations.
