Noon lecture

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On 03.08.2009 at 12:20 in S8, there is the following noon lecture:

Maximal equilateral sets

Konrad Swanepoel

Abstract

In the study of extremal situations, it is often fruitful to consider maximal objects of smallest size. For example, instead of considering the maximum number of pairwise non-overlapping translates of a convex body C that simultaneously touch C (the translative kissing number), one may ask for the minimum size of a maximal family of such translates, and arrive at the important notion of the blocking number of C, introduced by Zong.

In extremal graph theory, instead of asking for the maximum number ex(n;H) of edges of a graph with n vertices that does not contain a graph H, one may consider the minimum number sat(n;H) of edges of an H-saturated graph with n vertices; i.e. a graph that does not contain H, but if any new edge is added, will contain H.

In a similar spirit, we consider small maximal equilateral sets in finite-dimensional normed spaces, especially those whose norms are close to the p-norm.

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