# Mathematical Sciences Research Institute

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# Seminar

Combinatorial Fixed Point Theorems Working Group: Diameter of convex sets via graphs with large girth and small independence number December 05, 2017 (02:00 PM PST - 03:00 PM PST)
Parent Program: Geometric and Topological Combinatorics MSRI: Baker Board Room
Speaker(s) Eva Kopecka (Leopold-Franzens Universität Innsbruck)
Description No Description
Video
Abstract/Media

Let K be a compact convex set in R^d  which is an intersection of halfspaces defined by at most two coordinates. Let Q be the smallest axes-parallel box containing K.

We show that when the dimension d grows, the ratio of the diameters (diam Q/diam K) of the two sets can be arbitrarily large. How large exactly is open.

In Hilbert space every closed convex subset is contractive, that is, it is the fixed point set of a 1-Lipschitz mapping. In l_p-spaces, p not equal to 2, the contractive sets are known to be precisely the closed convex sets which are an intersection of halfspaces defined by at most two coordinates.