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Watch a 59-minute mathematical seminar presentation exploring the fundamental aspects and surprising properties of Funk geometry, delivered at the Colloque des sciences mathématiques du Québec. Delve into how the Funk metric relates to the Hilbert metric and hyperbolic geometry within convex bodies. Examine various problems in Funk geometry that connect to and enhance well-known theorems and conjectures in convex geometry, including the Blaschke-Santaló inequality, Mahler conjecture, and Schaeffer's dual girth conjecture. Learn about the relationships between Funk geometry and the Colbois-Verovic volume entropy conjecture, polyhedral combinatorics, and Minkowski billiards, featuring insights from collaborative research with Constantin Vernicos and Cormac Walsh.
