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  Counting lattice points in moduli spaces of quadratic differentials

Delecroix, V., Goujard, É., Zograf, P., & Zorich, A. (2023). Counting lattice points in moduli spaces of quadratic differentials. In D. Beliaev, & S. Smirnov (Eds.), ICM international congress of mathematicians 2022 July 6-14. Vol. 3: Sections 1-4 (pp. 2196-2211). Berlin: EMS Press.

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Item Permalink: https://hdl.handle.net/21.11116/0000-000F-77E0-E Version Permalink: https://hdl.handle.net/21.11116/0000-000F-77E1-D
Genre: Conference Paper

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Delecroix-Goujard-Zograf-Zorich_Counting lattice points in moduli spaces of quadratic differentials_2023.pdf (Publisher version), 633KB
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Zorich_Korrenspondenz_2024.pdf (Correspondence), 65KB
 
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 Creators:
Delecroix, Vincent, Author
Goujard, Élise, Author
Zograf, Peter, Author
Zorich, Anton1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Abstract: We show how to count lattice points represented by square-tiled surfaces in the moduli spaces of meromorphic quadratic differentials with simple poles on complex algebraic curves. We demonstrate the versatility of the lattice point count on three different examples, including evaluation of Masur–Veech volumes of the moduli spaces of quadratic differentials, computation of asymptotic frequencies of geodesic multicurves on hyperbolic surfaces, and asymptotic enumeration of meanders with a fixed number of minimal arcs.

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Language(s): eng - English
 Dates: 2023
 Publication Status: Issued
 Pages: 16
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.4171/icm2022/56
 Degree: -

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Title: International Congress of Mathematicians
Place of Event: Online
Start-/End Date: 2022-07-06 - 2022-07-14

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Title: ICM international congress of mathematicians 2022 July 6-14. Vol. 3: Sections 1-4
Source Genre: Proceedings
 Creator(s):
Beliaev, Dmitry, Editor
Smirnov, Stanislav, Editor
Affiliations:
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Publ. Info: Berlin : EMS Press
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 2196 - 2211 Identifier: ISBN: 978-3-98547-061-7
ISBN: 978-3-98547-561-2
DOI: 10.4171/ICM2022-3