%0 Journal Article %A DeMarco, Laura G. %D 2011 %T The conformal geometry of billiards %U https://indigo.uic.edu/articles/journal_contribution/The_conformal_geometry_of_billiards/10771409 %2 https://indigo.uic.edu/ndownloader/files/19284059 %K billiards %K Riemann %X 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. %I University of Illinois at Chicago