Abstract:
Gromov-Witten invariants count isolated stable holomorphic maps from a Riemann surface into a symplectic manifold subject to point-wise constraints. This count leads to a sequence of numbers labelled by the genus, the homology class, and a finite collection of cohomology classes. This sequence can be organized in a formal power series in several variables - the so-called Gromov-Witten potential. In order to compute the Gromov-Witten invariants, one is looking for algebraic relations between the coefficients of the Gromov-Witten potential. In some cases this can be done by invoking modularity properties of the Gromov-Witten potentials.