Masur–Veech volumes, frequencies of simple closed geodesics, and intersection numbers of moduli spaces of curves

Autor: Vincent Delecroix, Elise Goujard, Peter Zograf, Anton Zorich

Publikováno v: Duke Mathematical Journal
Duke Mathematical Journal, Duke University Press, 2021, 170 (12), pp.2633-2718. ⟨10.1215/00127094-2021-0054⟩
Duke Mathematical Journal, Duke University Press, In press
Duke Mathematical Journal, 2021, 170 (12), pp.2633-2718. ⟨10.1215/00127094-2021-0054⟩

We express the Masur-Veech volume and the area Siegel-Veech constant of the moduli space $\mathcal{Q}_{g,n}$ of genus $g$ meromorphic quadratic differentials with $n$ simple poles as polynomials in the intersection numbers of $\psi$-classes with expl

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fb73d25793d466c5cdd909573ad20b99
https://doi.org/10.1215/00127094-2021-0054

Contribution of one-cylinder square-tiled surfaces to Masur-Veech volumes

Autor: null Philip ENGEL, null Anton ZORICH, null Peter ZOGRAF, null Elise GOUJARD, null Vincent DELECROIX

Publikováno v: Asterisque
Asterisque, 2020, Quelques aspects de la théorie des systèmes dynamiques: un hommage à Jean-Christophe Yoccoz. I, 415 (415), pp.223--274. ⟨10.24033/ast.1107⟩
Asterisque, Société Mathématique de France, 2020, Quelques aspects de la théorie des systèmes dynamiques: un hommage à Jean-Christophe Yoccoz. I, pp.223--274. ⟨10.24033/ast.1107⟩

We compute explicitly the absolute contribution of square-tiled surfaces having a single horizontal cylinder to the Masur-Veech volume of any ambient stratum of Abelian differentials. The resulting count is particularly simple and efficient in the la

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::92b1ca58e04dcfdd20760ffed03d69fa
https://hal.science/hal-02482058

Conjectural large genus asymptotics of Masur-Veech volumes and of area Siegel-Veech constants of strata of quadratic differentials

Autor: Anton Zorich, Peter Zograf, Vincent Delecroix, Elise Goujard, Amol Aggarwal

Publikováno v: Arnold Mathematical Journal
Arnold Mathematical Journal, Springer, 2020, 6 (2), pp.149--161
Arnold Mathematical Journal, 2020, 6 (2), pp.149--161

We state conjectures on the asymptotic behavior of the Masur-Veech volumes of strata in the moduli spaces of meromorphic quadratic differentials and on the asymptotics of their area Siegel-Veech constants as the genus tends to infinity.
10 pages

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::25a9011318ad56e87a2fbbe35be66193
http://arxiv.org/abs/1912.11702

Enumeration of meanders and Masur-Veech volumes

Autor: Elise Goujard, Anton Zorich, Peter Zograf, Vincent Delecroix

Publikováno v: Forum of Mathematics, Pi
Forum of Mathematics, Pi, Professor Robert Guralnick Department of Mathematics|University of Southern California|Los Angeles|CA 90089-2532|USA, 2020, 8, pp.e4. ⟨10.1017/fmp.2020.2⟩

A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back to H. Poincar\'e and naturally appear in various are

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4e994c41776fca4ea65507efc719a1a9
http://arxiv.org/abs/1705.05190

Siegel-Veech constants for strata of moduli spaces of quadratic differentials

Autor: Elise Goujard

Publikováno v: Geometric And Functional Analysis
Geometric And Functional Analysis, 2015, 25 (5), pp.1440-1492
link.springer.com
Geometric and Functional Analysis

We present an explicit formula relating volumes of strata of meromorphicquadratic differentials with at most simple poles on Riemann surfacesand counting functions of the number of flat cylinders filled by closedgeodesics in associated flat metric wi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c66424717d3503cc64cf901ddf4b2d4a
https://hal.archives-ouvertes.fr/hal-00995027v4/document