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Graduate Seminar

Clive Newstead
Carnegie Mellon University
Title: Hairy balls and ham sandwiches

Abstract: Point-set topology studies spaces up to homeomorphism. For many purposes this notion of equivalence is too strong, but by studying spaces up to homotopy equivalence we can assign algebraic invariants that allow us to prove some interesting results. One of these is the so-called hairy ball theorem, which says that any tangent vector field on a 2n-sphere must vanish somewhere. Another is the ham sandwich theorem, which says that given any collection of n objects of finite measure in n-space, there is an (n-1)-hyperplane which slices each object exactly in half. This talk aims to give a picture of what algebraic topology is all about, without getting too bogged down in details.

Date: Thursday, November 14, 2013
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Brian Kell