Oliver Leigh: The r-ELSV Formula via Virtual Localisation

Abstract

For a fixed positive integer \(r\), a stable map is said to have "divisible ramification" if the order of every ramification locus is divisible by \(r\). In this talk I'll review the theory of stable maps with divisible ramification and show how this leads to a new geometric framework from which to view and prove Zvonkine's \(r\)-ELSV formula. Namely, that the natural moduli space which parametrises these objects gives rise to a natural Hurwitz-type theory where the techniques of virtual localisation can be applied.