Infinite Analysis Seminar Tokyo

Seminar information archive ~07/03Next seminarFuture seminars 07/04~

Date, time & place Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.)

2025/07/14

15:30 (仮)-16:30 (仮)   Room #056 (Graduate School of Math. Sci. Bldg.)
Danilo Lewański (University of Trieste)
A spin on Gromov-Witten / Hurwitz correspondence and integrability
(English)
[ Abstract ]
Hurwitz numbers enumerate branched coverings of Riemann surfaces and provide a rich sandbox of examples for enumerative geometry and neighbouring areas. Surprisingly, there is a formula that connects them to the intersection theory of the moduli spaces of stable curves: the ELSV formula. Furthermore, these numbers enjoy an integrability of type 2D-Toda as they can be expressed as vacuum expectations in the Fock space, result that has been later employed in the GW/Hurwitz correspondence.

A spin-off from the research on the mirror symmetry on Calabi-Yau 3-folds led to the spin generation of Hurwitz numbers via topological recursion. Over time this result has been generalised in different directions, including the Hurwitz count of Riemann surfaces with a spin structure, which are conjecturally determining Gromov-Witten invariants of surfaces with smooth canonical divisor. This led once more to the link with integrability, this time of type BKP.