SEMINARIO DE MATEMÁTICAS ITAM

A cargo de: Francis Edward Su, Harvey Mudd College (USA)

Título: A polytopal generalization of Sperner's lemma

Abstract:
Sperner's lemma is a statement about labelled triangulations of simplices, that is the combinatorial equivalent of the Brouwer fixed point theorem. With J. DeLoera and E. Peterson, we prove a polytopal generalization of Sperner's lemma to polytopes in two different ways, one constructive and one non-constructive, and give applications of this result: to cake-cutting, to minimal triangulations of polytopes, and to the game of Hex.