Super stable maps
Enno Keßler (MPI-M Bonn)

J-holomorphic curves or pseudoholomorphic curves are maps from Riemann
surfaces to symplectic manifolds satisfying the Cauchy-Riemann equations.
J-holomorphic curves are of great interest because they allow to construct
invariants of symplectic manifolds and those invariants are deeply related to
topological superstring theory. 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 couple the equations of classical J-holomorphic curves
with a Dirac equation for spinors and are critical points of the
superconformal action. The compactification of the moduli space of super J-
holomorphic curves via super stable maps might, in the future, lead to a
supergeometric generalization of Gromov-Witten invariants.

Based on arXiv:2010.15634 [math.DG] and arXiv:1911.05607 [math.DG], joint with
Artan Sheshmani and Shing-Tung Yau.