A tour through Mirzakhani’s work on moduli spaces of Riemann surfaces

DOI10.1090/bull/1687zbMath1452.32003arXiv1905.01753OpenAlexW3005466694MaRDI QIDQ5122995

Alex Wright

Publication date: 25 September 2020

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.01753

zbMATH Keywords

moduli of Riemann surfaces

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15)

Related Items (19)

Masur-Veech volumes, frequencies of simple closed geodesics, and intersection numbers of moduli spaces of curves ⋮ Bose–Einstein condensation on hyperbolic spaces ⋮ Random hyperbolic surfaces of large genus have first eigenvalues greater than \(\frac{3}{16}-\epsilon\) ⋮ Benjamini-Schramm convergence and spectra of random hyperbolic surfaces of high genus ⋮ A random cover of a compact hyperbolic surface has relative spectral gap \(\frac{3}{16}-\varepsilon\) ⋮ Unicellular maps vs. hyperbolic surfaces in large genus: simple closed curves ⋮ Near optimal spectral gaps for hyperbolic surfaces ⋮ Large genus asymptotics for lengths of separating closed geodesics on random surfaces ⋮ Effective mapping class group dynamics. I: Counting lattice points in Teichmüller space ⋮ GOE statistics on the moduli space of surfaces of large genus ⋮ Towards optimal spectral gaps in large genus ⋮ The Asymptotic Statistics of Random Covering Surfaces ⋮ The limit set of non-orientable mapping class groups ⋮ Enumerative geometry of surfaces. Abstracts from the workshop held June 13--19, 2021 (hybrid meeting) ⋮ A model for random three-manifolds ⋮ Short geodesic loops and \(L^p\) norms of eigenfunctions on large genus random surfaces ⋮ The diameter of random Belyĭ surfaces ⋮ Bootstrap bounds on closed hyperbolic manifolds ⋮ Length statistics of random multicurves on closed hyperbolic surfaces

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