MS Seminar (Mathematics - String Theory)

Speaker: Enno Kessler (Max-Planck-Institut für Mathematik in den Naturwissenschaften)
Title: Super Stable Maps and Super Gromov-Witten Invariants
Date (JST): Tue, Mar 05, 2024, 13:30 - 15:00
Place: Seminar Room A
Abstract: J-holomorphic curves or pseudoholomorphic curves are maps from Riemann
surfaces to almost Kähler manifolds satisfying the Cauchy-Riemann equations.
The moduli space of J-holomorphic curves has a natural compactification using
stable maps. Moduli spaces of stable maps are of great interest because they
allow to construct invariants of the target manifold and those invariants are
deeply related to topological superstring theory.

In this talk, I want to report on a supergeometric generalization of J-
holomorphic curves, stable maps and Gromov-Witten invariants where the domain
is a super Riemann surface. Super Riemann surfaces have first appeared in
superstring theory as generalizations of Riemann surfaces with an additional
anti-commutative dimension. Super J-holomorphic curves are solutions to a
system of partial differential equations on the underlying Riemann surface
coupling the Cauchy-Riemann equation with a Dirac equation for spinors. I will
explain how to construct moduli spaces of super J-holomorphic curves and super
stable maps in genus zero via super differential geometry and geometric
analysis. Motivated by the super moduli spaces I give an algebro-geometric
proposal for super Gromov-Witten invariants satisfying generalized Kontsevich-
Manin axioms.