David Kern: Derived geometric Field Theory for orbifold quasimap theory

Abstract

The Gromov–Witten invariants of a smooth projective variety produce a Cohomological Field Theory, a structure that can be expressed as an algebra over the operad of homologies of the moduli stacks of stable curves. Mann–Robalo showed that, using derived geometry and the phenomenon of brane actions discovered by Toën, it can be lifted from the cohomological setting to the categorical and even the geometric one.

When the target is a stack, it is known from Abramovich–Graber–Vistoli that the CohFT is only exhibited on (a “cyclotomic” decomposition of) its inertia stack. I will explain how the orbifold structure of the target can be used to extend the GW stability condition to the family of quasimap theories on it, and how Mann–Robalo’s construction adapts to a geometric CohFT in which the cyclotomic inertia appears naturally from operadic data.