Mathematical Sciences: Analysis on Loop Space

Ezra Getzler将继续他的工作，为循环空间开发一系列分析工具。这涉及到Sobolev空间，对数Sobolev不等式，布朗运动，奇异积分估计，deRham上同调，Feynman- Kac公式。这项研究构成了一个更大的项目的一部分，以确定局部指标理论是否与狄拉克算子内在相连，或者它是否是一个更大的代数理论的一部分。同样地，狄拉克指数与环空间的等变上同调之间的关系可以是一个更大理论的一部分。

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.