Berlin-Hamburg-Seminar am 15.4.2019

Mihai Munteanu (HU Berlin) Essential tori in spaces of symplectic embeddings

In this talk, we will introduce recent work (joint with Julian Chaidez) in which we study the singular homology of spaces of symplectic embeddings involving symplectic ellipsoids. More specifically, we will show how certain n-torus families of symplectic embeddings between 2n-dimensional ellipsoids become homologically nontrivial if certain inequalities involving symplectic invariants are satisfied.

Wolfgang Schmaltz (Gießen) Gromov-Witten Axioms for Symplectic Manifolds via Polyfold Theory

Polyfold theory, as developed by Hofer, Wysocki, and Zehnder, is a relatively new approach to resolving transversality issues that arise in the study of J-holomorphic curves in symplectic geometry. I will explain some of the philosophy of the polyfold theoretic approach to defining the Gromov-Witten invariants for all closed symplectic manifolds.
In 1994 Kontsevich and Manin stated the Gromov-Witten axioms, given as a list of formal relations between the Gromov-Witten invariants. From the point of view of polyfold theory, I will prove several of the Gromov-Witten axioms for curves of arbitrary genus for all closed symplectic manifolds.