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Graduate Seminar
Chris Cox CMU 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 fixedpoint theorem, the hairyball 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 envyfree division problems and the game of Hex. Date: Tuesday, February 13, 2018 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Son Van 