The Funk Metric in Convex Geometry and Related Fields
Explore the Funk metric and its connections to various aspects of geometry in this 53-minute lecture by Dmitry Faifman. Delve into the relationship between Funk geometry and convex geometry, affine geometry, Finsler billiards, and the combinatorics of convex polyhedra. Learn about the newly observed property of projective invariance of the Funk metric and its implications. Examine results linking Funk geometry to the Blaschke-Santalo inequality, Mahler's conjecture, the Colbois-Verovic conjecture in Hilbert geometry, Schaeffer's dual girth conjecture, and Kalai's flag number conjecture for symmetric polyhedra. Gain insights from Faifman's research, including joint work with C. Vernicos and C. Walsh, presented as part of the Thematic Programme on "Geometry beyond Riemann: Curvature and Rigidity" at the Erwin Schrödinger International Institute for Mathematics and Physics.