### Flag Approximability of convex bodies and volume entropy of Hilbert geometries

Geometry and Topology Seminar

13th December 2022, 2:00 pm – 3:00 pm

Fry Building, 2.04

(joint work with C. Walsh) Following our title, this talk will seemingly have two distinct parts. We will begin with approximabilties of a convex body which are numbers reflecting the difficulty to approximate that body by polytopes. Afterwards we will look at Hilbert geometries which are generalisations of the projective model of the Hyperbolic geometry (otherwise known as Klein model). These geometries are based on the cross-ratio, and they are defined in open convex bodies. We will survey some basic facts about them and then turn to the volume of balls of large radius. More specifically will focus on the volume entropy and end up back to the flag approximability.

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