Ramifications of Hurwitz theory, KP integrability and quantum curves

2015/12/31 by A. Alexandrov, D. Lewanski, S. Shadrin · 32 citations
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Geometry and complex manifolds #Hurwitz matrix #Monotone polygon #Point (geometry) #Quantum #Spectral properties #hep-th #math-ph #math.AG #math.CO #math.MP

paper · pdf · doi:10.1007/jhep05(2016)124

published in Journal of High Energy Physics 2016(5) (Springer Nature) · 30 pages, references updated, minor corrections

openalex publication_date 2016/05/01 · arxiv created 2016/05/09 · openalex created_date 2016/06/24 · arxiv updated 2017/08/22 · openalex updated_date 2026/08/05

Abstract

In this paper we revisit several recent results on monotone and strictly monotone Hurwitz numbers, providing new proofs. In particular, we use various versions of these numbers to discuss methods of derivation of quantum spectral curves from the point of view of KP integrability and derive new examples of quantum curves for the families of double Hurwitz numbers.

Citations

• Polynomiality of Hurwitz numbers, Bouchard–Mariño conjecture, and a new proof of the ELSV formula
• Enumerative Geometry, Tau-Functions and Heisenberg–Virasoro Algebra

Cited by

• Quantum Curves in the Context of Symplectic Duality