Selected Topics in Applied Topology
by
Dmitri Shakhmatov
Ehime University, Japan

In a series of three workshop lectures we will give examples of how general and geometric topology can be applied to produce results in neighbouring areas of mathematics. Topics covered will include:

1. linearity of quasi-states on C^*-algebras,
2. realations between stable rank and covering dimension of C^*-algebras,
3. geometric and topological properties of capacities,
4. transforming compact perfect sets of arbitrary small (possibly zero) capacity into sets of arbitrary big capacity via homeomorphisms, weak forms of diffeomorphisms, and quasi-conformal maps,
5. Wiener criterion and the classical Dirichlet problem in potential theory and partial differential equations,
6. topology and algebra.

Date received: July 15, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caap-05.