Non-archimedean Quantum K-theory and Gromov-Witten invariants

Motivated by mirror symmetry and the enumeration of curves with boundaries, it is desirable to develop a theory of Gromov-Witten invariants in the setting of non-archimedean geometry. I will explain our recent works in this direction. Our approach differs from the classical one in algebraic geometry via perfect obstruction theory. Instead, we build on our previous works on the foundation of derived non-archimedean geometry, the representability theorem and Gromov compactness. We obtain numerical invariants by passing to K-theory or motivic cohomology. We prove a list of natural geometric relations between the stacks of stable maps, directly at the derived level, with respect to elementary operations on graphs, namely, products, cutting edges, forgetting tails and contracting edges. They imply the corresponding properties of numerical invariants. The derived approach produces highly intuitive statements and functorial proofs. Furthermore, its flexibility allows us to impose not only simple incidence conditions for marked points, but also incidence conditions with multiplicities. Joint work with M Porta.

The synchronous discussion for Tony Yue Yu’s  talk is taking place not in zoom-chat, but at https://tinyurl.com/2022-03-18-ty (and will be deleted after ~3-7 days).