Mathematics Colloquia and Seminars

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After examining one or more proofs of the Brouwer fixed-point theoem, we'll examine the Schauder fixed-point theorem: Let A be a non-empty convex subset of a Banach space X. Let Y be a compact subset of A. Then a continuous map from A to Y has a fixed point. We'll then outline the proof of Kakutani's fixed-point theorem, and if time remains, we'll briefly discuss an application to the existence of Nash equilibria for zero-sum games.