April 20, 2017

Transversally Elliptic Operators and K-theory

The class of (pseudo-) differential operators transversally elliptic with respect to a Lie group action on a manifold was introduced by M. Atiyah in the 70s. He also made an attempt to obtain a formula which calculates the index of such operators by topological means. This class of operators is interesting both from the point of view of geometry and analysis, but particularly by its relations with representation theory of Lie groups. In the 90s, N. Berline and M. Vergne have obtained a certain very complicated index formula. However, this did not stop further attempts to obtain something more reasonable and more useful in applications. I will try to explain the background of the theory and a different approach to an index formula.

Tea at 3:30 pm in SC 1425. (Contact Person: Bruce Hughes)