Departmental Colloquium
Liviu Nicolaescu
University of Notre Dame
Counting Morse functions on S^2
Abstract: Two Morse functions on a smooth manifold M are called equivalent
if we can obtain one from the other by global changes of coordinates on M
and R (the real numbers). V.I. Arnold has computed the number of such equivalence
classes when M=S^1, and formulated a precise conjecture concerning the
asymptotics of these numbers when M= S^2.
I will explain how to describe the generating function of the numbers of
Morse functions on S^2 in terms of certain elliptic integrals, and then
how to use this to prove Arnold's conjectured asymptotics.
Friday March 16, 2007 at 3:00 PM in SEO 636