Ezra Getzler will continue his work on developing a collection of analytic tools for loop spaces. This involves Sobolev spaces, logarithmic Sobolev inequalities, Brownian motion, singular integral estimates, deRham cohomology, Feynman- Kac formulae. This research forms part of a larger program to determine whether local index theory is intrinsically connected with Dirac operators or if it is part of a much bigger algebraic theory. Equivalently the relations between the the Dirac index and equivariant cohomology of the loop space may be part of a larger theory.
