Colloquium: Computing a categorical Gromov-Witten invariant

Location：Room 302, Library

Speaker: Junwu Tu, ShanghaiTech University

Abstract: We compute the g = 1, n = 1 B-model Gromov-Witten invariant of an elliptic curve E directly from the derived category of coherent sheaves on E. More precisely, we carry out the computation of the categorical Gromov-Witten invariant defined by Costello using as target a cyclic A-infinity model due to Polishchuk. This is the first non-trivial computation of a positive genus categorical GromovWitten invariant, and the result agrees with the prediction of mirror symmetry: it matches the classical (non-categorical) Gromov-Witten invariants of a symplectic 2-torus computed by Dijkgraaf. This is a joint work with Andrei Caldararu.