Időpont: 2025. november 25. 12:30

Helyszín: Riesz-terem, Bolyai Épület, 6720 Szeged, Aradi vértanúk tere 1.

Absztrakt: A theorem of Sas states that in plane among convex bodies of unit area, ellipses are hardest to approximate in terms of area difference with an inscribed convex polygon with a fixed number of vertices. He also showed that the only extremizers of this problem are the ellipses. Macbeath, in a classical theorem, generalized this result for higher dimensions and proved that the volume difference between a convex body and a largest volume inscribed convex polytope with a fixed number of vertices is maximal, relative to the volume of the body, for Euclidean balls.

Our goal in this talk to investigate normed variants of this problem, and find largest volume polytopes with a fixed number of vertices and insribed in the unit ball of the norm, have the largest/smallest Busemann volume, Holmes-Thompson volume, Gromov's mass and mass* as defined by the norm. Joint work with Zsolt Lángi.