Billiards in Conics Revisited

Explore the fascinating world of billiards in conics in this illuminating mathematics colloquium talk. Delve into the optical properties of conics, tracing their history back to classical antiquity. Discover how the concept of billiard reflection in an ideal mirror relates to the completely integrable billiard system inside an ellipse. Learn about the foliation of ellipse interiors by confocal ellipses serving as caustics, where light rays tangent to a caustic remain tangent after reflection. Examine classic results and their geometric implications, including the Ivory lemma, which proves the equality of diagonals in curvilinear quadrilaterals formed by confocal ellipse and hyperbola arcs. Explore applications such as the renowned Poncelet Porism from projective geometry, along with its lesser-known offshoots like the Poncelet Grid theorem and related circle patterns and configuration theorems. Gain insights into these complex mathematical concepts through the expertise of Penn State's Sergei Tabachnikov in this comprehensive Stony Brook Mathematics Colloquium presentation.