Abstract:
A
few years ago -- following a suggestion by I. M. Gelfand--
I discovered an intriguing connection between
the topological
degree of a map from the circle
into itself and its Fourier coefficients. This relation is easily
justified when
the map is smooth. However, the
situation turns out to be much more delicate if one assumes
only continuity,
or even Holder continuity. I will present recent developments and open
problems. I will
also discuss new
estimates for the degree of maps from S^n into S^n,
leading to unusual characterizations of
Sobolev
spaces. The initial motivation for this direction of research came
from the analysis of
the Ginzburg-
Landau model
occurring in superconductivity.
.
November 11th, Wednesday, 5:00-6:00
pm
Mathematics 520
Tea will be
served at 4:30pm