Title of Jonathan Rosenberg's course:
Applications of noncommutative topology in geometry and string theory.
Abstract:
The purpose of this course will be to give an introduction to ways
in which noncommutative topology can be applied to geometry and
topology in the usual sense (as studied by topologists, for example)
and to string theory. Topics to be discussed will include the
following:
1. What is noncommutative topology, what is noncommutative geometry,
and what's the difference between them? What are some of the
techniques available for studying them?
2. Applications of noncommutative topology, especially C*-algebras
of groupoids, to the study of group actions on manifolds,
geometry of foliations, stratified spaces, and singular spaces.
3. An introduction to twisted K-theory, why it appears in physics,
and what it has to do with noncommutative topology.
4. Some applications of noncommutative topology and noncommutative
geometry that have appeared in the recent physics literature.