MINICOURSE 3: Topics in mathematical billiards and geometrical optics

par Sergei Tabachnikov (Pennsylvania State University)

vendredi 27 mai 2016, 17:00 → 18:00 Europe/Paris

In this mini-series of talks, I shall focus on completely integrable billiards and their geometrical applications. In particular, old and new results around the Poncelet Porism will be described, including the Poncelet grid, the related circle patterns, and the centers of mass of the Poncelet polygons. I shall relate Ivory's Lemma (discovered by J. Ivory in his study of the gravitational attraction of ellipsoids) with billiards in conics and quadratic surfaces. I shall also discuss problems of free-form ray optics, including the Levi-Civita theorem (constructing a mirror that takes one normal family of rays to the other). I shall explain the "periscope theorem" that describes the transformations of parallel beams of light after reflection in a pair of mirrors. Open problems will be emphasized.