Algebraic & Geometric Topology Volume 20, issue 5 (2020)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Pillowcase covers: counting Feynman-like graphs associated with quadratic differentials

Elise Goujard and Martin Möller

Algebraic & Geometric Topology 20 (2020) 2451–2510

DOI: 10.2140/agt.2020.20.2451

Bibliography

1	A Aggarwal, Large genus asymptotics for volumes of strata of abelian differentials, J. Amer. Math. Soc. 33 (2020) 941 MR4155217
2	J S Athreya, A Eskin, A Zorich, Right-angled billiards and volumes of moduli spaces of quadratic differentials on ℂP¹, Ann. Sci. École Norm. Sup. 49 (2016) 1311 MR3592359
3	J Böhm, K Bringmann, A Buchholz, H Markwig, Tropical mirror symmetry for elliptic curves, J. Reine Angew. Math. 732 (2017) 211 MR3717092
4	D Chen, M Möller, Nonvarying sums of Lyapunov exponents of abelian differentials in low genus, Geom. Topol. 16 (2012) 2427 MR3033521
5	D Chen, M Möller, A Sauvaget, D Zagier, Masur–Veech volumes and intersection theory on moduli spaces of abelian differentials, Invent. Math. 222 (2020) 283 MR4145791
6	D Chen, M Möller, D Zagier, Quasimodularity and large genus limits of Siegel–Veech constants, J. Amer. Math. Soc. 31 (2018) 1059 MR3836563
7	V Delecroix, E Goujard, P Zograf, A Zorich, Masur–Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves, preprint (2019) arXiv:1908.08611
8	F Diamond, J Shurman, A first course in modular forms, 228, Springer (2005) MR2112196
9	R Dijkgraaf, Mirror symmetry and elliptic curves, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 149 MR1363055
10	P Engel, Hurwitz theory of elliptic orbifolds, I, preprint (2017) arXiv:1706.06738
11	A Eskin, M Kontsevich, A Zorich, Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmüller geodesic flow, Publ. Math. Inst. Hautes Études Sci. 120 (2014) 207 MR3270590
12	A Eskin, H Masur, A Zorich, Moduli spaces of abelian differentials : the principal boundary, counting problems, and the Siegel–Veech constants, Publ. Math. Inst. Hautes Études Sci. 97 (2003) 61 MR2010740
13	A Eskin, A Okounkov, Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials, Invent. Math. 145 (2001) 59 MR1839286
14	A Eskin, A Okounkov, Pillowcases and quasimodular forms, from: "Algebraic geometry and number theory" (editor V Ginzburg), Progr. Math. 253, Birkhäuser (2006) 1 MR2263191
15	E Goujard, Siegel–Veech constants for strata of moduli spaces of quadratic differentials, Geom. Funct. Anal. 25 (2015) 1440 MR3426059
16	E Goujard, Volumes of strata of moduli spaces of quadratic differentials: getting explicit values, Ann. Inst. Fourier (Grenoble) 66 (2016) 2203 MR3580171
17	E Goujard, M Möller, Counting Feynman-like graphs : quasimodularity and Siegel–Veech weight, J. Eur. Math. Soc. 22 (2020) 365 MR4049220
18	V G Kac, Infinite-dimensional Lie algebras, Cambridge Univ. Press (1990) MR1104219
19	M Kaneko, D Zagier, A generalized Jacobi theta function and quasimodular forms, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 165 MR1363056
20	S Kerov, G Olshanski, Polynomial functions on the set of Young diagrams, C. R. Acad. Sci. Paris Sér. I Math. 319 (1994) 121 MR1288389
21	H Masur, A Zorich, Multiple saddle connections on flat surfaces and the principal boundary of the moduli spaces of quadratic differentials, Geom. Funct. Anal. 18 (2008) 919 MR2439000
22	A Okounkov, R Pandharipande, Gromov–Witten theory, Hurwitz theory, and completed cycles, Ann. of Math. 163 (2006) 517 MR2199225
23	R Ríos-Zertuche, An introduction to the half-infinite wedge, from: "Mexican mathematicians abroad: recent contributions" (editors N Bárcenas, F Galaz-García, M Moreno Rocha), Contemp. Math. 657, Amer. Math. Soc. (2016) 197 MR3466453
24	A Sauvaget, Volumes and Siegel–Veech constants of ℋ(2G − 2) and Hodge integrals, Geom. Funct. Anal. 28 (2018) 1756 MR3881834
25	J P Serre, Topics in Galois theory, 1, Jones & Bartlett (1992) MR1162313
26	S Shadrin, L Spitz, D Zvonkine, On double Hurwitz numbers with completed cycles, J. Lond. Math. Soc. 86 (2012) 407 MR2980918
27	A Zorich, Flat surfaces, from: "Frontiers in number theory, physics, and geometry, I" (editors P Cartier, B Julia, P Moussa, P Vanhove), Springer (2006) 437 MR2261104