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 Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

The conformal geometry of billiards

Author(s): Laura DeMarco
Journal: Bull. Amer. Math. Soc. 48 (2011), 33-52.
MSC (2010): Primary 37D50, 32G15
Posted: October 15, 2010
MathSciNet review: 2738905
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Abstract | References | Similar articles | Additional information

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 $ \mathrm{SL}_2\mathbb{R}$ 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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Additional Information:

Laura DeMarco
Affiliation: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago
Email: demarco@math.uic.edu

DOI: 10.1090/S0273-0979-2010-01322-7
PII: S 0273-0979(2010)01322-7
Received by editor(s): July 19, 2010
Posted: October 15, 2010
Copyright of article: Copyright 2010, American Mathematical Society




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