Billiards and Teichmüller curves

McMullen, Curtis

doi:10.1090/bull/1782

Billiards and Teichmüller curves
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by Curtis T. McMullen;

Bull. Amer. Math. Soc. 60 (2023), 195-250

DOI: https://doi.org/10.1090/bull/1782

Published electronically: November 28, 2022

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Abstract:

A Teichmüller curve $V \subset \mathcal {M}_g$ is an isometrically immersed algebraic curve in the moduli space of Riemann surfaces. These rare, extremal objects are related to billiards in polygons, Hodge theory, algebraic geometry and surface topology. This paper presents the six known families of primitive Teichmüller curves that have been discovered over the past 30 years, and a selection of open problems.

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Billiards and Teichmüller curves
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