University of Georgia
Mathematics Department Colloquium
Adam Parusinski
University of Angers, France
November 2, 2000
Abstract: Let x(t) be a trajectory of the gradient
of a real analytic function and suppose that x_0 is a limit point of x(t).
We present a proof of the
gradient conjecture of Rene Thom, which states that the secants of
x(t) at x_0 also have a limit. Actually we show a stronger statement: The
radial
projection of x(t) from x_0 onto the unit sphere has finite length.
(This is joint work with Krzysztof Kurdyka and Tadeusz Mostowski.)