Time: April 15, 2026 (Wednesday) 12:30 pm

Location: Riesz lecture hall, Bolyai Building, Aradi vértanúk tere 1., Szeged, Hungary

Abstract: First, we establish Blaschke–Santaló-type inequalities for r-ball bodies. These results allow us to extend earlier work on analogues of the Kneser–Poulsen conjecture, specifically for intersections of balls under uniform contractions in Euclidean d-space. As a direct consequence, we obtain a proof of Alexander’s conjecture in the setting of uniform contractions.

We then introduce the class of basic r-ball polyhedra in Euclidean d-space and analyze their face structure. In this context, we prove an analogue of McMullen’s Upper Bound Theorem. Finally, we show that every basic r-ball polyhedron is globally rigid with respect to its inner dihedral angles.

Time: April 22, 2026 (Wednesday) 12:00 pm

Location: Riesz lecture hall, Bolyai Building, Aradi vértanúk tere 1., Szeged, Hungary

Abstract: A well-known conjecture asserts that the isotropic constant is maximized among n-dimensional convex bodies by the simplex. Supporting evidence for this conjecture is provided by a result due to Rademacher: a simplicial polytope P that is locally maximizing has to be a simplex. In this talk, we discuss necessary conditions for a polytope P to be a local maximizer of the isotropic constant and present several strengthenings and variations of Rademacher's result. In particular, we show that the existence of a simplicial vertex is sufficient to conclude that P is a simplex. In the centrally symmetric setting, the assumption that P has a simplicial vertex implies that P is a cross-polytope, and the assumption that P is a zonotope with a cubical zone implies that P is a cube.