Speaker: Sergei Tabachnikov

Date:  November 16th, Thursday, 12:00-1:00 pm (time zone of Topeka, Kansas).

Link: Sent to registered participants by e-mail one hour before the talk.

Abstract:  Optical properties of conics have been known since the classical antiquity. The reflection in an ideal mirror is also known as the billiard reflection. The interior of an ellipse is foliated by confocal ellipses that are its caustics: a ray of light tangent to a caustic remains tangent to it after reflection (“caustic” means burning in Greek). I shall present these classic results and some of their geometric consequences, including  the Poncelet Porism, a famous theorem of projective geometry that has recently celebrated its bicentennial, and designs of traps for parallel beams of light.

About the speaker:  Sergei Tabachnikov received his PhD from Moscow State University in 1987, and since 1990 he has taught at American universities, currently at Penn State. His mathematical tastes are diverse: he has worked in differential geometry, differential topology, and dynamical systems. Although he himself does not program, he appreciates and loves experimental mathematics. He has served as editor-in-chief of Experimental Mathematics in 2013–2019 and as deputy director of ICERM at Brown University in 2013–2015. He believes that it is important to popularize mathematics at all levels, and he has been involved in this activity all his professional life. His book "Mathematical Omnibus", coauthored with Dmitry Fuchs, is one such popularization effort, and the book has been translated into German, Russian, and Japanese. Sergei has also published two books on mathematical billiards, a book on projective differential geometry (jointly with Valentin Ovsienko), and a book, Polynomials, for high-school students (in Russian). Since 2021, Sergei has served as a co-editor-in-chief of the Mathematical Intelligencer.