Some questions about polytopes

Convex polytopes are among the most fundamental geometric objects, and have numerous applications ranging from art, through engineering, to applied mathematics and computer science.

In this talk we will consider several questions about polytopes, focusing on combinatorial and geometric aspects. In particular, we will mention questions about the realization spaces of polytopes, Voronoi's conjecture on parllelohedra, face numbers of cubical polytopes and the VC-dimension of polytopes.