Mathematics Colloquium
Thursday, October 19, 1995, 4:00pm
102 Bradley Hall
Professor Paul Baum
Penn State University
speaks on
Statement and Proof of the Atiyah-Singer Index Theorem
Abstract. The Atiyah-Singer Index Theorem has been at the center
of a great deal of research in geometry, topology and operator
algebras. It is of current interest to physicists in computing
Seiberg-Witten invariants in topological quantum field theory.
The Atiyah-Singer Index Theorem states that two integers associated
to an elliptic operator on a compact manifold, the "analytic index" and
the "topological index," are in fact the same. The analytic index measures
the difference in dimensions of the kernel and cokernel of the operator.
The topological index is computed using the symbol of the operator which
is given by local data and only depends on the highest order terms of the operator.
In this talk, we will discuss low-dimensional examples
and give an elementary proof of Atiyah-Singer which illustrates that it
is a corollary of the Bott Periodicity phenomena in the K-theory
of operator algebras. This talk will be accessible to a general mathematical
audience.
Tea. High tea will be served at 3:30pm in the Lounge.
Emmy's. Certain refreshments will be available at the Emmy's after the talk.
Host. Jody Trout will be the host, anybody interested in having dinner with the speaker should contact Jody (Ext. 6-2958).