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Colloquium, Spring 2005

Day: Thursday May 26th Time: 4:00pm Place: BH 227 Title: The Isoperimetric Inequality via Brunn-Minkowski Speaker: Andrew Richardson, WWU If you were to ask a middle school student to enclose the largest area with a fixed length of string, it is more than likely that he or she would mold the string into a circle. While this two-dimensional application of the isoperimetric inequality has been long known, few mathematicians are aware of how this inequality is intimately related to an interwoven web of inequalities stretching through not only geometry, but also analysis. While the statement of the inequality is simple, and its implications are quite intuitive, many proofs of this inequality are difficult. In the late nineteenth century, Hermann Brunn and Hermann Minkowski, inspired by the purely geometric issues around the isoperimetric inequality, developed the "Brunn-Minkowski" inequality. In this talk, I will explore the isoperimetric inequality and some of its applications, prove a generalized version of the Brunn-Minkowski inequality and show how it implies the isoperimetric inequality in just a few easy-to-follow steps. Cookies: In BH 300 at 3:30pm.