Download this article
 Download this article For screen
For printing
Recent Issues

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
The combinatorial formula for open gravitational descendents

Ran J Tessler

Geometry & Topology 27 (2023) 2497–2648
Bibliography
1 A Alexandrov, Open intersection numbers, matrix models and MKP hierarchy, J. High Energy Phys. (2015) 042 MR3340741
2 A Alexandrov, A Buryak, R J Tessler, Refined open intersection numbers and the Kontsevich–Penner matrix model, J. High Energy Phys. (2017) 123 MR3650694
3 A Bawane, H Muraki, C Rim, Open KdV hierarchy and minimal gravity on disk, Phys. Lett. B 783 (2018) 183 MR3840816
4 R Bott, L W Tu, Differential forms in algebraic topology, 82, Springer (1982) MR658304
5 A Buryak, Equivalence of the open KdV and the open Virasoro equations for the moduli space of Riemann surfaces with boundary, Lett. Math. Phys. 105 (2015) 1427 MR3395226
6 A Buryak, Open intersection numbers and the wave function of the KdV hierarchy, Mosc. Math. J. 16 (2016) 27 MR3470575
7 A Buryak, E Clader, R J Tessler, Open r–spin theory, II : The analogue of Witten’s conjecture for r–spin disks, preprint (2018) arXiv:1809.02536
8 A Buryak, E Clader, R J Tessler, Open r–spin theory, I : Foundations, Int. Math. Res. Not. 2022 (2022) 10458 MR4458550
9 A Buryak, A Netser Zernik, R Pandharipande, R J Tessler, Stationary open ℂℙ1 descendent theory, II : The open GW/H correspondence, in preparation
10 A Buryak, R J Tessler, Matrix models and a proof of the open analog of Witten’s conjecture, Comm. Math. Phys. 353 (2017) 1299 MR3652492
11 A Buryak, A N Zernik, R Pandharipande, R J Tessler, Open ℂℙ1 descendent theory, I : The stationary sector, Adv. Math. 401 (2022) 108249 MR4387849
12 D Cimasoni, N Reshetikhin, Dimers on surface graphs and spin structures, I, Comm. Math. Phys. 275 (2007) 187 MR2335773
13 P Deligne, D Mumford, The irreducibility of the space of curves of given genus, Inst. Hautes Études Sci. Publ. Math. 36 (1969) 75 MR262240
14 R Dijkgraaf, H Verlinde, E Verlinde, Loop equations and Virasoro constraints in nonperturbative two-dimensional quantum gravity, Nuclear Phys. B 348 (1991) 435 MR1083914
15 R Dijkgraaf, E Witten, Developments in topological gravity, preprint (2018) arXiv:1804.03275
16 K Fukaya, K Ono, Arnold conjecture and Gromov–Witten invariant for general symplectic manifolds, from: "The Arnoldfest" (editors E Bierstone, B Khesin, A Khovanskii, J E Marsden), Fields Inst. Commun. 24, Amer. Math. Soc. (1999) 173 MR1733575
17 J Harris, I Morrison, Moduli of curves, 187, Springer (1998) MR1631825
18 T J Jarvis, Geometry of the moduli of higher spin curves, Internat. J. Math. 11 (2000) 637 MR1780734
19 T J Jarvis, T Kimura, A Vaintrob, Moduli spaces of higher spin curves and integrable hierarchies, Compositio Math. 126 (2001) 157 MR1827643
20 D Johnson, Spin structures and quadratic forms on surfaces, J. London Math. Soc. 22 (1980) 365 MR588283
21 D Joyce, D–manifolds, d–orbifolds and derived differential geometry : a detailed summary, preprint (2012) arXiv:1208.4948
22 D Joyce, On manifolds with corners, from: "Advances in geometric analysis" (editors S Janeczko, J Li, D H Phong), Adv. Lect. Math. 21, International (2012) 225 MR3077259
23 P W Kasteleyn, Dimer statistics and phase transitions, J. Mathematical Phys. 4 (1963) 287 MR153427
24 S Katz, C C M Liu, Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc, from: "The interaction of finite-type and Gromov–Witten invariants" (editors D Auckly, J Bryan), Geom. Topol. Monogr. 8, Geom. Topol. Publ. (2006) 1 MR2402818
25 M Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992) 1 MR1171758
26 G Kuperberg, An exploration of the permanent-determinant method, Electron. J. Combin. 5 (1998) 46 MR1663576
27 C C M Liu, Moduli of J–holomorphic curves with Lagrangian boundary conditions and open Gromov–Witten invariants for an S1–equivariant pair, J. Iran. Math. Soc. 1 (2020) 5 MR4528678
28 E Looijenga, Cellular decompositions of compactified moduli spaces of pointed curves, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 369 MR1363063
29 M Mirzakhani, Weil–Petersson volumes and intersection theory on the moduli space of curves, J. Amer. Math. Soc. 20 (2007) 1 MR2257394
30 A Okounkov, R Pandharipande, Gromov–Witten theory, Hurwitz numbers, and matrix models, from: "Algebraic geometry, I" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 325 MR2483941
31 R Pandharipande, J P Solomon, R J Tessler, Intersection theory on moduli of disks, open KdV and Virasoro, preprint (2014) arXiv:1409.2191
32 B Safnuk, Combinatorial models for moduli spaces of open Riemann surfaces, preprint (2016) arXiv:1609.07226
33 B Safnuk, Topological recursion for open intersection numbers, Commun. Number Theory Phys. 10 (2016) 833 MR3636676
34 J P Solomon, R J Tessler, Graded spin surfaces and the open Arf invariant, in preparation
35 J P Solomon, R J Tessler, Intersection theory on the moduli space of graded Riemann surfaces with boundary, in preparation
36 J P Solomon, S B Tukachinsky, Differential forms on orbifolds with corners, preprint (2020) arXiv:2011.10030
37 K Strebel, Quadratic differentials, 5, Springer (1984) MR743423
38 E Witten, Two-dimensional gravity and intersection theory on moduli space, from: "Surveys in differential geometry" (editors H B Lawson Jr., S T Yau), Lehigh Univ. (1991) 243 MR1144529
39 E Witten, Algebraic geometry associated with matrix models of two-dimensional gravity, from: "Topological methods in modern mathematics" (editors L R Goldberg, A V Phillips), Publish or Perish (1993) 235 MR1215968
40 A N Zernik, Equivariant open Gromov–Witten theory of ℝℙ2mℂℙ2m, preprint (2017) arXiv:1709.09483
41 A N Zernik, Moduli of open stable maps to a homogeneous space, preprint (2017) arXiv:1709.07402
42 D Zvonkine, Strebel differentials on stable curves and Kontsevich’s proof of Witten’s conjecture, preprint (2002) arXiv:math/0209071