On Hadwiger’s covering functional for the simplex and cross-polytope

Speaker: Lian Yanlu (School of Mathematics, Hangzhou Normal University)

Venue: Room 203, Building 2, Haina Court, Zijingang Campus

Abstract: In 1957, Hadwiger made a conjecture that every n-dimensional convex body can be covered by 2^n translations of its interior. The Hadwiger's covering functional is the smallest positive number r such that K can be covered by m translations of rK. Due to Zong's program, we study the Hadwiger's covering functional for the simplex and the cross-polytope. In this paper, we give upper bounds for the Hadwiger's covering functional of the simplex and the cross-polytope.