| 概要 | In this lecture, I will explain the deep relations which exist between probability theory and Ito's calculus on one hand, and the index theorem on the other hand. I will illustrate this connection by the proof of the index theorem itself, in which measures on the loop space of a manifold should be properly interpreted as differential forms, and also by the construction of the hypoelliptic Laplacian, in which a functional analytic version of Ito's formula plays a key role. |