The conformal geometry of billiards

Laura Demarco

doi:10.1090/S0273-0979-2010-01322-7

The conformal geometry of billiards

Laura Demarco^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

This article provides an introduction to some recent results in billiard dynamics. We present results that follow from a study of compact Riemann surfaces (equipped with a holomorphic 1-form) and an SL₂R action on the moduli spaces of these surfaces. We concentrate on the progress toward classification of "optimal" billiard tables, those with the simplest trajectory structure.

Original language	English (US)
Pages (from-to)	33-52
Number of pages	20
Journal	Bulletin of the American Mathematical Society
Volume	48
Issue number	1
DOIs	https://doi.org/10.1090/S0273-0979-2010-01322-7
State	Published - 2011

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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AB - This article provides an introduction to some recent results in billiard dynamics. We present results that follow from a study of compact Riemann surfaces (equipped with a holomorphic 1-form) and an SL2R action on the moduli spaces of these surfaces. We concentrate on the progress toward classification of "optimal" billiard tables, those with the simplest trajectory structure.

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The conformal geometry of billiards

Abstract

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