Sperner's Lemma, Brouwer's Fixed Point Theorem, birthday cakes, and
roommates

by

Aaron Reite

Abstract: This talk will concern applications of Sperner's Lemma - a rather simple combinatorial result regarding triangulations of simplices. Most notably we will give an elementary proof of Brouwer's Fixed Point Theorem using Sperner's Lemma (and no algebraic topology!) We will then briefly discuss some applications of Sperner's Lemma to fair division.