Polynomiality of orbifold Hurwitz numbers, spectral curve, and a new proof of the Johnson-Pandharipande-Tseng formula

T. Miwa, M. Jimbo, E. Date, Solitons. Differential equations, symmetries and infinite-dimensional algebras. Translated from the 1993 Japanese original by Miles Reid. Cambridge Tracts in Mathematics, 135. Cambridge University Press, Cambridge, 2000

2000

Earlier work this paper cites.

A. Okounkov, Toda equations for Hurwitz numbers. Math. Res. Lett. 7

2000

Earlier work this paper cites.

T. Ekedahl, S. Lando, M. Shapiro, and A. Vainshtein, Hurwitz numbers and intersections on moduli spaces of curves , Invent. Math. 146 (2001), no. 2, 297–-327

2001

Earlier work this paper cites.

I.P. Goulden, D.M. Jackson, R. Vakil, Towards the geometry of double Hurwitz numbers , Adv. Math. 198 (2005), 43–92

2005

Cited alongside, same era.

B. Eynard, N. Orantin, Invariants of algebraic curves and topological expansion , Commun. Number Theory Phys. 1 (2007), no. 2, 347-–452

2007

Cited alongside, same era.

P. Johnson, R. Pandharipande, H.-H. Tseng Abelian Hurwitz–Hodge integrals , Mich. Math. J. 60

2011

Cited alongside, same era.

G. Borot, B. Eynard, N. Orantin, Abstract loop equations, topological recursion, and applications, arXiv: 1303.5808

Cited in the paper.

G. Borot, S. Shadrin, Blobbed topological recursion: properties and applications, arXiv: 1502.00981

Cited in the paper.

N. Do, O. Leigh, P. Norbury, Orbifold Hurwitz numbers and Eynard-Orantin invariants , arXiv: 1212.6850

Cited in the paper.

P. Dunin-Barkowski, M. Kazarian, N. Orantin, S. Shadrin, L. Spitz, Polynomiality of Hurwitz numbers, Bouchard-Mariño conjecture, and a new proof of the ELSV formula , arXiv: 1307.4729

Cited in the paper.

P. Dunin-Barkowski, N. Orantin, S. Shadrin, L. Spitz, Identification of the Givental formula with the spectral curve topological recursion procedure , arXiv: 1211.4021

Cited in the paper.

B. Eynard, Invariants of spectral curves and intersection theory of moduli spaces of complex curves , arXiv: 1110.2949

Cited in the paper.

B. Eynard, A short overview of the “Topological recursion” , arXiv: 1412.3286

Cited in the paper.

P. Johnson, Equivariant Gromov-Witten theory of one dimensional stacks , arXiv: 0903.1068

Cited in the paper.

P. Johnson, Double Hurwitz numbers via the infinite wedge , arXiv: 1008.3266

Cited in the paper.

V. Bouchard, D. Hernàndez Serrano, X. Liu, M. Mulase, Mirror symmetry for orbifold Hurwitz numbers , J. Differ. Geom. 98 (2014), 375–423

2014

Later among the works it cites.

D. Lewanski, A. Popolitov, S. Shadrin, D. Zvonkine, Chiodo formulas for the r r -th roots and topological recursion , preprint 2015

2015

Closest in time.

S. Shadrin, L. Spitz, D. Zvonkine, Equivalence of ELSV and Bouchard-Mariño conjectures for r r -spin Hurwitz numbers , Math. Ann. 361

2015

Closest in time.