Columbia Mathematics Department Colloquium


`` Can you hear the winding number?"


 Haim Brezis  

Rutgers, Paris 6, and Technion



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