Abstract:

In this talk, I will discuss the combined asymptotics of normalized disconnected relative Gromov-Witten invariants of a smooth algebraic curve of genus at least two. Using the Okounkov-Pandharipande correspondence between stationary Gromov-Witten invariants and Hurwitz numbers with completed cycles, we derive a combined asymptotic expansion as the degree and the genus of the moduli space tend to infinity simultaneously. The expansion is stratified by the offset of the partition in the Okounkov-Pandharipande sum from the fully ramified partition(d). The terms corresponding to partitions with a long first row contribute at the polynomial level, with the coefficient of each level controlled by a character polynomial in the parts of the ramification profiles. The remaining terms are smaller than any polynomial order.