Talk page
Title:
Mirror symmetry for orbifold Hurwitz numbers
Speaker:
Abstract:
In recent years, it has been found that many enumerative geometric problems have a common feature: they have a mirror symmetric counterpart which is governed by a universal integral recursion formula due to Eynard and Orantin. The key ingredient to the mirror theory is the existence of a spectral curve (also known as ""mirror curve"" in this context). Once the spectral curve mirror to a given counting problem is determined, the integral recursion uniquely calculates all generating functions of the corresponding enumerative invariants. In this talk I will show that the mirror counterparts to orbifold Hurwitz numbers satisfy the integral recursion, with spectral curve given by the ""r-Lambert curve"". I will also argue that orbifold Hurwitz numbers can be obtained in the """"infinite framing limit"""" of orbifold Gromov-Witten theory of [C3/(Z/rZ)], thus shedding some light on the appearance of the recursion for orbifold Hurwitz numbers and its relation with the so-called remodeling conjecture for Gromov-Witten theory on toric orbifolds.
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