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Sperner’s lemma: generalizations and applications (Oleg Musin, UT Rio Grande Valley)
December 4, 2018 @ 12:15 pm - 1:10 pm
The classical Sperner – KKM (Knaster – Kuratowski – Mazurkiewicz) lemma has many applications in combinatorics, algorithms, game theory and mathematical economics. In this talk we consider generalizations of this lemma as well as Gale’s colored KKM lemma and Shapley’s KKMS theorem. It is shown that spaces and covers can be much more general and the boundary KKM rules can be substituted by more weaker boundary assumptions. These generalizations of Sperner’s lemma rely on homotopy invariants of covers that in fact are obstructions for extending a cover of a subspace A in X to a cover of X.