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TITLE / TITRE

(Almost) all roads lead to Funk geometry

ABSTRACT /R脡SUM脡聽

The Funk metric is a lesser-known cousin of the Hilbert metric in the interior of a convex body, which in turn generalizes (the Beltrami-Klein model of) hyperbolic geometry. After presenting the basics of the Funk metric and some of its surprising properties, I will describe several problems in Funk geometry which relate to, generalize and strengthen various well-known theorems and conjectures in convex geometry (such as the Blaschke-Santal贸 inequality, the Mahler conjecture, and Schaeffer's dual girth conjecture), the Colbois-Verovic volume entropy conjecture in Hilbert geometry, polyhedral combinatorics, and Minkowski billiards. Partially based on a joint work with Constantin Vernicos and Cormac Walsh.

PLACE /LIEU聽
Hybride - CRM, Salle / Room 5340, Pavillon Andr茅 Aisenstadt