| 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. |
