Mathematics

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.A master version of slides can be found at the website (talks usually present an abridged version): https://sites.google.com/view/wolfgang-schmaltz/home The talk will include a significant introductory first part, making it suitable for the non experts.