Berlin-Hamburg-Seminar am 18.10.2016
Yoel Groman (Columbia University, New York) Symplectic invariants on open manifolds
I will discuss various constructions such as Gromov Witten theory, symplectic cohomology, the wrapped Fukaya category etc., on geometrically bounded open symplectic manifolds and show that these are truly symplectic invariants. As time will permit I will discuss classical applications to problems such as existence results for periodic orbits and distinguishing symplectic manifolds. The talk will be based mostly on arXiv:1510.04265.
Dmitry Tonkonog (Uppsala Universitet) Wall-crossing for mutations of Lagrangian tori and symplectic cohomology
Given a Lagrangian torus with an attached Lagrangian disk, a procedure called mutation produces a new Lagrangian torus out of it. Iterating this procedure allows to construct infinitely many monotone Lagrangian tori in del Pezzo surfaces, which was done by Vianna. We prove the wall-crossing formula which solves the problem of enumerating Maslov index 2 holomorphic disks on these tori. Time permitting, I will also talk about the related Laurent phenomenon, and what it has to do with the symplectic cohomology of certain domains. This is joint work in progress with James Pascaleff.