<\/p>\n\n\n\n
Time: <\/strong>17:00 (Israel Time)<\/p>\n\n\n\n Location: <\/strong>In Room 614 of the Science & Education Building, University of Haifa and on Zoom<\/p>\n\n\n\n Recording:<\/strong><\/p>\n\n\n\n https:\/\/us02web.zoom.us\/rec\/share\/11wbNQ9drctg3GJjEHL784aCI9iAczSpRsOuPha69BFsCmeQl6KXclBCWauaFMNF.mJ2eReCfMakLrdia<\/a><\/p>\n\n\n\n Abstract.<\/strong><\/p>\n\n\n\n We place a light source inside a smooth convex billiard table (or mirror). The n<\/em>-th caustic by reflection is the envelope of the light rays after n<\/em> reflections. Theorem: each of these caustics, for a generic point light source, has at least 4 cusps. This is a billiard version of “Jacobi\u2019s Last Geometric Statement”, concerning the number of cusps of the conjugate locus of a point on a convex surface, proved so far only in the n=1<\/em> case. I will show various proofs, using different ideas, including the curve shortening flow and Legendrian knot theory. I will also show computer experiments supporting the conjecture that for an elliptical billiard table and any position of the light source, other than the foci, the n<\/em>-th caustic by reflection has exactly 4 cusps. <\/p>\n\n\n\n (Joint work with Serge Tabachnikov of Penn State) <\/p>\n\n\n\n ZOOM COORDINATES:<\/strong><\/p>\n\n\n\n https:\/\/us02web.zoom.us\/j\/84987591026?pwd=aTJWcFlOSldKck5leGt2d25CYkRqZz09<\/a><\/p>\n\n\n\n Meeting ID: 849 8759 1026<\/p>\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" Time: 17:00 (Israel Time) Location: In Room 614 of the Science & Education Building, University of Haifa and on Zoom Recording: https:\/\/us02web.zoom.us\/rec\/share\/11wbNQ9drctg3GJjEHL784aCI9iAczSpRsOuPha69BFsCmeQl6KXclBCWauaFMNF.mJ2eReCfMakLrdia Abstract. We place a light source inside a smooth convex billiard table (or mirror). The n-th caustic by…
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