Graduate Student / Postdoc Seminar

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Least Volume Bodies of Constant Width

Speaker: Ryan Hynd

Location: Warren Weaver Hall 1302

Date: Friday, March 30, 2012, 1 p.m.

Synopsis:

A convex set is said to have constant width 1 if the projection of the body onto every line has length 1. It is well known that, in any dimension, the ball of diameter 1 encloses the most volume of any constant width set. A famous theorem of Lesbesgue and Blaschke asserts that the Reuleaux triangle has least area amongst any two dimensional set of constant width. In this talk, we present a few ideas that might be used to approach the minimum problem in dimension greater than two.