Cool Logic

Ezra Schoen (ILLC)

An Almost Constructive Proof of Brouwer's Fixed Point Theorem

March 31st at 17:00, in Zoom

As a young mathematician, Brouwer gained prominence by proving a number of fundamental theorems in topology, the most famous of which is his eponymous fixed point theorem. However, Brouwer would later come to reject this theorem as not intutionistically acceptable. In this talk, I will (briefly) sketch the proof of Brouwer's fixed point theorem as it is given in most textbooks, and present an alternative, 'almost constructive' proof based on Sperner's lemma. I will also discuss how this second proof can be used to obtain intuitionistically valid variants of the fixed point theorem. Zoom link:[eight nine four]16398787 (Replace string enclosed in square brackets by the three numerals)