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.
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