Symplectic Geometry
Organizers: Mohammed Abouzaid, Eleny Ionel, and Jae Hee Lee
There is tea prior to the talk in the 4th floor lounge.
The Northern California Symplectic Geometry Seminar usually meets on the first Monday of each month, and alternates between Stanford and Berkeley.
Past Events
Abstract
Sabloff duality is an analogue of Poincaré duality for Legendrian contact homology, which is a Floer-theoretic invariant of Legendrian knots. In this talk, I will tell you about an A-infinity enhancement of Sabloff duality. If time permits, I will also mention higher homotopies for this enhanced…
Pseudo-Anosov flows, originally introduced by Thurston, are a broad class of hyperbolic flows on 3-manifolds that are Anosov except along a finite link of singular closed orbits. A longstanding conjecture states that any 3-manifold carries only finitely many transitive pseudo-Anosov flows, up to…
Abstract: I will discuss Floer theoretical invariants of arbitrary open contact manifolds in their relation with invariants of contactomorphisms.
This is a work in progress with Kiran Ajij, Mahan Mg, Dishant Pancholi and Leonid Polterovich.
Abstract: A symplectic homeomorphism is a C^0 limit of symplectic diffeomorphisms; a topological symplectic manifold is a manifold with an atlas whose transition maps are symplectic homeomorphisms. I will explain recent joint work showing that all such manifolds are bi-Lipschitz. As a…
The s-cobordism theorem uses simple homotopy equivalences, a refinement of homotopy equivalences detected by Whitehead torsion, to distinguish h-cobordant manifolds. More recently, it has appeared in symplectic geometry through the work of Abouzaid and Kragh, in connection with the topology of…
Contact homeomorphisms are points in the closure of the (compactly supported) contactomorphism group in the homeomorphism group under the C^0-topology. Recently, Dimitroglou Rizell and Sullivan showed that the images of closed Legendrians under contact homeomorphisms are…
The moduli space of rank n local systems on a Riemann surface S famously admits "cluster coordinates," which are now part of the "higher Teichmuller theory" of Fock and Goncharov. It was later discovered by Gaiotto, Moore, and Neitzke that these coordinate charts can be identified with the…
There are several approaches to defining SFT in the presence of Legendrian/Lagrangian boundary conditions; I will discuss the approach of Cieliebak-Latschev-Mohnke which uses string topology operations defined by Chas-Sullivan. I will focus on the implementation of this approach for Legendrian…
In this talk we will prove that there are precisely two embedded exact Lagrangian fillings of the standard Legendrian Hopf link, up to compactly supported Hamiltonian isotopy. It was known that the standard Legendrian Hopf link admitted at least two such Lagrangian fillings: we show these are…