Title : Hairy balls, fixed points and coffee!!!
Abstract :
Singularities occur naturally everywhere around us, may it be an eye of a
cyclone where there is no wind at all, or the north pole where the
different time zones converge. The purpose of this talk is to study these
patterns mathematically. Hairy ball theorem precisely states that: An even
dimensional sphere does not possess any continuous nowhere vanishing
tangent vector field". The basic notions of tangent vector field,
fundamental groups, some concepts of point set topology will be discussed
(at least intuitively) and then a geometric proof of the theorem will be
studied. It will be followed by a few applications in the end.
3:00pm
4:00pm
5:00pm
Time:
2:00pm
Location:
Ramanujan Hall, Department of Mathematics
Description:
Title : Hairy balls, fixed points and coffee!!!
Abstract :
Singularities occur naturally everywhere around us, may it be an eye of a
cyclone where there is no wind at all, or the north pole where the
different time zones converge. The purpose of this talk is to study these
patterns mathematically. Hairy ball theorem precisely states that: An even
dimensional sphere does not possess any continuous nowhere vanishing
tangent vector field". The basic notions of tangent vector field,
fundamental groups, some concepts of point set topology will be discussed
(at least intuitively) and then a geometric proof of the theorem will be
studied. It will be followed by a few applications in the end.