• Corpus ID: 235195907

Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture

  title={Elements of spin Hurwitz theory: closed algebraic formulas, blobbed topological recursion, and a proof of the Giacchetto-Kramer-Lewanski conjecture},
  author={Alexander Alexandrov and Sergey Viktorovich Shadrin},
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 sums which are given by Orlov’s hypergeometric solutions of the 2component BKP hierarchy. We derive the closed algebraic formulas for the correlation functions associated with these tau-functions, and under reasonable analytical assumptions we prove the loop equations (the blobbed topological… 
1 Citations
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


A new spin on Hurwitz theory and ELSV via theta characteristics
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
Weighted Hurwitz Numbers and Topological Recursion
The KP and 2D Toda $$\tau $$ τ -functions of hypergeometric type that serve as generating functions for weighted single and double Hurwitz numbers are related to the topological recursion programme.
Generalized Br\'ezin-Gross-Witten tau-function as a hypergeometric solution of the BKP hierarchy
In this paper, we prove that the generalized Brézin–Gross–Witten taufunction is a hypergeometric solution of the BKP hierarchy with simple weight generating function. We claim that it describes a
Spin Hurwitz numbers and topological quantum field theory
Spin Hurwitz numbers count ramified covers of a spin surface, weighted by the size of their automorphism group (like ordinary Hurwitz numbers), but signed $\pm 1$ according to the parity of the
Explicit closed algebraic formulas for Orlov-Scherbin $n$-point functions
We derive a new explicit formula in terms of sums over graphs for the npoint correlation functions of general formal weighted double Hurwitz numbers coming from the Orlov–Scherbin partition
Abstract loop equations, topological recursion, and applications
We formulate a notion of abstract loop equations, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The
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
Weighted Hurwitz numbers and topological recursion: An overview
Multiparametric families of hypergeometric $\tau$-functions of KP or Toda type serve as generating functions for weighted Hurwitz numbers, providing weighted enumerations of branched covers of the
Blobbed topological recursion: properties and applications
  • G. Borot, S. Shadrin
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2016
Abstract We study the set of solutions (ωg,n ) g⩾0,n⩾1 of abstract loop equations. We prove that ω g,n is determined by its purely holomorphic part: this results in a decomposition that we call
Invariants of algebraic curves and topological expansion
For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties.