September 30, 2008

Speaker: Kenneth Hoover

Title: The Hairy Ball Theorem


Abstract:  Can you comb your hair without parting it and without any misplaced hairs?  Of course you can!  For instance, just take the ill-advised "comb-over" as a case in point.  But now imagine that your head was detached from your body and covered completely with hair.  Could you do it then?  Some thought may reveal that the answer to this question is "no", but did you know that the fields of topology and differential geometry have already addressed this question from a mathematical standpoint?  The famous hairy ball theorem states that there exists no continuous nonvanishing vector field on the sphere.  What does this have to do with combing your hair?  Come to the talk and find out!