The spin Gromov-Witten/Hurwitz correspondence

Abstract: In 2006, Okounkov and Pandharipande established a correspondence between two theories of counting maps between curves. Gromov-Witten theory constructs a moduli space of stable maps and considers intersection numbers of natural classes on this space. Hurwitz theory counts the number of maps with given ramification data over all points in the target. The Gromov-Witten theory of a surface with positive geometric genus can be localised to a curve in that surface, and this obtains a spin structure, leading to spin Gromov-Witten theory of curves. The Hurwitz side also has a natural spin analogue, and Lee conjectured these theories correspond in a similar manner. In this talk, I will introduce the notions of spin Gromov-Witten theory and spin Hurwitz theory and give an outline of the spin Gromov-Witten/Hurwitz correspondence for the projective line. I will also explain relations to the (small) 2BKP integrable hierarchy, which is the analogue of the 2D Toda lattice hierarchy in the non-spin case. This talk is based on joint work with Alessandro Giacchetto, Danilo Lewański, and Adrien Sauvaget.

HEP - theorymathematical physicsalgebraic geometrycombinatoricsexactly solvable and integrable systems

Audience: researchers in the discipline

IBS-CGP Mathematical Physics Seminar

Series comments: Registration is required at cgp.ibs.re.kr/activities/talkregistration