Polyhedra, functional analysis and approximation theory

Time: 9:00 - 10:00 AM, October 24th, 2023 (Tuesday)

Location: Room 612, building A6, Institute of Mathematics (18 Hoang Quoc Viet, Cau Giay, Hanoi)

Abstract: This talk will focus on some combinatorial properties of polytopes (a polytope is the convex hull of a finite set). For example, given natural numbers d, v, e, is there a d-dimensional polytope with v vertices and e edges? Surprisingly perhaps, this is impossible if 2e-dv lies in either of the intervals [1,d-3] or [d+3,2d-7].

Our interest in polytopes originally arose from a problem about approximation in Banach spaces. We will begin by briefly outlining this history, demonstrating the underlying unity of different branches of mathematics.