Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Philippe G. Ciarlet and Prof. Roderick Wong

Cohomology at a Fixed Scale for Metric Spaces

by
Professor Nat Smale
University of Utah and
Department of Mathematics
City University of Hong Kong

Date: Nov 25, 2009 (Wednesday)
Time:4:30 pm to 5:30 pm
Venue: Room B6605 (College Conference Room)
Blue Zone, Level 6, Academic Building
City University of Hong Kong

ABSTRACT: We will discuss a "scaled cohomology" theory for compact metric spaces, that gives a way of quantiying topological type features that can be seen at a specified scale. One goal is to develop a theory analogous to the deRham cohomology and Hodge theory for smooth manifolds, that will work in a more general setting, without the assumption of smoothness. Thus a notion of the Hodge Laplacian is defined in this setting, and a Hodge Theorem would state that a cohomology class is represented by a harmonic function. Some examples will be given, and we will look at some conditions that imply when such a theorem holds. This is joint work with Steve Smale, Thomas Schick and Laurent Bartholdi.

** All interested are welcome **

For enquiry: 2788-9816