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!