• Corpus ID: 233209972

A new spin on Hurwitz theory and ELSV via theta characteristics

@inproceedings{Giacchetto2021ANS,
  title={A new spin on Hurwitz theory and ELSV via theta characteristics},
  author={Alessandro Giacchetto and Reinier Kramer and Danilo Lewa'nski},
  year={2021}
}
We study spin Hurwitz numbers, which count ramified covers of the Riemann sphere with a sign coming from a theta characteristic. These numbers are known to be related to Gromov-Witten theory of Kähler surfaces and to representation theory of the Sergeev group, and are generated by BKP tau-functions. We use the latter interpretation to give polynomiality properties of these numbers and we derive a spectral curve which we conjecture computes spin Hurwitz numbers via a new type of topological… 

Tables from this paper

Relations for quadratic Hodge integrals via stable maps
. Following Faber-Pandharipande, we use the virtual localization formula for the moduli space of stable maps to P 1 to compute relations between Hodge integrals. We prove that certain generating
Integrals of $\psi$-classes on twisted double ramification cycles and spaces of differentials
We prove a closed formula for the integral of a power of a single ψ-class on strata of k-differentials. In many cases, these integrals correspond to intersection numbers on twisted double
Genus one free energy contribution to the quartic Kontsevich model
We prove a formula for the genus one free energy F (1) of the quartic Kontsevich model for arbitrary ramification by working out a boundary creation operator for blobbed topological recursion. We
A natural basis for intersection numbers
We advertise elementary symmetric polynomials ei as the natural basis for generating series Ag,n of intersection numbers of genus g and n marked points. Closed formulae for Ag,n are known for genera
KP hierarchy for Hurwitz-type cohomological field theories
Abstract. We generalise a result of Kazarian regarding Kadomtsev-Petviashvili integrability for single Hodge integrals to general cohomological field theories related to Hurwitz-type counting
Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture
In this paper, we discuss the properties of the generating functions of spin Hurwitz numbers. In particular, for spin Hurwitz numbers with arbitrary ramification profiles, we construct the weighed

References

SHOWING 1-10 OF 81 REFERENCES
A square root of Hurwitz numbers
  • Junho Lee
  • Mathematics
    manuscripta mathematica
  • 2019
We exhibit a generating function of spin Hurwitz numbers analogous to (disconnected) double Hurwitz numbers that is a tau function of the two-component BKP (2-BKP) hierarchy and is a square root of a
A NOTE ON GUNNINGHAM’S FORMULA
  • Junho Lee
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 2018
Gunningham [‘Spin Hurwitz numbers and topological quantum field theory’, Geom. Topol. 20(4) (2016), 1859–1907] constructed an extended topological quantum field theory (TQFT) to obtain a closed
Polynomial solutions of the BKP hierarchy and projective representations of symmetric groups
  • Infinite-Dimensional Lie Algebras and Groups
  • 1989
Integrals of $\psi$-classes on twisted double ramification cycles and spaces of differentials
We prove a closed formula for the integral of a power of a single ψ-class on strata of k-differentials. In many cases, these integrals correspond to intersection numbers on twisted double
Topological recursion for Kadomtsev-Petviashvili tau functions of hypergeometric type
We study the n-point differentials corresponding to Kadomtsev–Petviashvili tau functions of hypergeometric type (also known as Orlov–Scherbin partition functions), with an emphasis on their
Around spin Hurwitz numbers
We present a review of the spin Hurwitz numbers, which count the ramified coverings with spin structures. They are related to peculiar Q Schur functions, which are actually related to characters of
Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials
We describe a conjectural formula via intersection numbers for the Masur-Veech volumes of strata of quadratic differentials with prescribed zero orders, and we prove the formula for the case when the
JT gravity and the ensembles of random matrix theory
We generalize the recently discovered relationship between JT gravity and double-scaled random matrix theory to the case that the boundary theory may have time-reversal symmetry and may have fermions
Topological recursion for Masur-Veech volumes.
We study the Masur--Veech volumes $MV_{g,n}$ of the principal stratum of the moduli space of quadratic differentials of unit area on curves of genus $g$ with $n$ punctures. We show that the volumes
Loop equations and a proof of Zvonkine's $qr$-ELSV formula
We prove the 2006 Zvonkine conjecture that expresses Hurwitz numbers with completed cycles in terms of intersection numbers with the Chiodo classes via the so-called $r$-ELSV formula, as well as its
...
...