Applications of Brouwer's Fixed Point Theorem

Wednesday, May 4, 2016 - 10:00am
111 MSB
Amanda Bright (Advisor: Prof. Konstantin Makarov)

This project focuses on one of the most influential theorems of the last century, Brouwer's fixed point theorem. First published in 1910, this theorem has found itself in the intersection of many different fields of mathematics along with physics and economics. This talk will explore some of the proofs involving homology, combinatorics (Sperner's lemma), and analysis (Milnor-Rogers), a generalization by Shizu Kakutani, and applications of the theorem including those of Nobel Prize winners Wassily Leontief and John Nash.