# Oliver Leigh: r-Spin Hurwitz numbers via Stable Maps with Divisible Ramification

**Time: **
Tue 2021-11-02 13.15 - 14.15

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, meeting ID: 921 756 1880)

**Participating: **
Oliver Leigh (Uppsala University)

**Abstract:** Hurwitz numbers enumerate smooth covers of the projective plane with a given set of ramification conditions. Classically, this set of conditions required all ramification to be of order 1. There are many beautiful and deep results related to classical Hurwitz numbers. This includes the ELSV formula, a link to Gromov-Witten theory, links to mathematical physics and links to topological recursion. A natural question to ask is: How many of these results hold when the condition "all ramificaiton is order 1" is replaced with "all ramificaiton is order *r*"? In this talk we will answer this quesion using the theory of stable maps with divisible ramification. This will include links to *r*-spin theory via Zvonkine’s *r*-ELSV formula and a discussion of the subtleties arising in this situation.