RIND seminar on Mathematical Physics and String Theory

Nov. 28, 2022 at 4 p.m. c.t. only via Zoom

Ilka Brunner (LMU München)
Nils Carqueville (Universität Wien)
Hans Jockers (JGU Mainz)
Peter Mayr (LMU München)
Simone Noja (Universität Heidelberg)
Ivo Sachs (LMU München)
Johannes Walcher (Universität Heidelberg)

Joint seminar series on Mathematical Physics and String Theory

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.