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Graduate Seminar

Chris Cox
Title: Sperner's lemma and applications

Abstract: In this talk, we'll look at a very simple result known as Sperner's lemma. Roughly, the result states that if one colors the vertices of a triangulation of a polygon with three colors, then, under reasonable assumptions, there will always be a rainbow triangle. This simple combinatorial theorem can be proved in about one line, but can be applied to prove powerful theorems such as Brouwer's fixed-point theorem, the hairy-ball theorem and even the Fundamental Theorem of Algebra. Time permitting, we will apply Sperner's lemma to prove these theorems and may also discuss applications to envy-free division problems and the game of Hex.

Date: Tuesday, February 13, 2018
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Son Van