Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Fixed point theorems

Student-Run Geometry/Topology Seminar

Speaker: Eddie Kim, UC Davis
Location: 2112 MSB
Start time: Thu, Apr 20 2006, 1:10PM

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.