November 6, 2020
Super Stable Maps.
J-holomorphic curves or pseudoholomorphic curves have been of great interest to mathematics since the discovery that J-holomorphic curves allow to construct invariants of symplectic manifolds by Gromov and that those invariants are related to topological superstring theory by Witten. A crucial step towards Gromov–Witten invariants is the compactification of the moduli space of J-holomorphic curves via stable maps which was first proposed by Kontsevich and Manin. In this talk, I want to report on a supergeometric generalization of J-holomorphic curves and stable maps where the domain is a super Riemann surface. Super Riemann surfaces have first appeared as generalizations of Riemann surfaces with anti-commutative variables in superstring theory. Super J-holomorphic curves and super stable maps couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and might ultimatively lead to a supergeometric generalization of Gromov-Witten invariants. Based on arXiv:2010.15634 & arXiv:1911.05607, joint with Artan Sheshmani and Shing-Tung Yau.