Fall 2010, Thursdays, Milner 216, 4:00-4:50 PM

Date: December 2

"  The Ham Sandwich Brotherhood "
  Aaron Goldsmith  


The Ham Sandwich (Stone-Tukey) Theorem says that anytime two hungry brothers settle a dispute over cutting a ham sandwich, there is a straight and fair cut, no matter how sloppily the pieces are arranged. Here, we define a ham sandwich to consist of two slices of bread and one slice of ham. More gory details to come.

We will use Borsuk-Ulam Theorem (Daddy) to present a proof of the Ham Sandwich Theorem, then introduce the brotherhood: Kakutani's Theorem, Lusternik-Schnirelmann Theorem, and Brouwer Fixed Point Theorem. The material should be easily grasped with a little topology and measure theory. Included will be as much history as is reasonable. Story time!