JUNIOR COLLOQUIUM

SPEAKER: Prof. Almut Burchard, University of Toronto

TITLE: Steiner symmetrization: Some new twists in an old story

ABSTRACT: Steiner symmetrization was invented in the 1830's as a tool for proving the isoperimetric inequality, that circles enclose the largest area among all planar curves of a given length. Since then, it has found many applications in Geometry, Mathematical Physics, and Functional Analysis.

In this talk I will describe Steiner's original argument and two recent results. The first concerns infinite sequences of Steiner symmetrizations that fail to converge to the ball, but still converge "in shape". The second bounds the perimeter of a set in R^d that has been subjected to Steiner symmetrization along d linearly independent directions. Time permitting, I will mention some open problems.

Pizza available at 3:00 p.m.