ICTP/SISSA Joint Colloquium (18 April 2007)

[Math]

ICTP/SISSA Joint Colloquium in Mathematics

Announcement



Wednesday, 18 April 2007, at 14.30 hrs.



Professor Haim Brezis

University of Paris 6 and Rutgers



Can you hear the degree of a map from the circle into itself?



Abstract:

Following a suggestion by I. M. Gelfand, and motivated by questions  
arising from the Ginzburg-Landau model - I discovered a few years  
ago, 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 extremely 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 leading to unusual characterizations of Sobolev  
spaces.  This also raises challenging questions connected to Gamma- 
convergence.

Venue:  ICTP Main Lecture Hall, Main Building, entrance level