Borsuk–Ulam Theorem and its applications

Abstract

The Borsuk-Ulam Theorem is a very well-known theorem in Topology. It has been studied extensively, and has a plethora of applications in combinatorics and topology. We will see a classic construction of the theorem and its proof, then look at some generalizations and other forms of proof directions, as well as some mirror theorems in combinatorics. We assume knowledge of basic homotopy and the theory surrounding the fundamental group.

This was a blackboard talk; written notes are available above.