XXVI Workshop on Geometric Methods in Physics 1-7.07.2007

Tilmann Wurzbacher

Differential geometry of free loop spaces: a direct approach to elliptic genera?

String theory predicts the existence of a "Ramond-Dirac operator" on the free loop space of a finite dimensional manifold and furthermore indicates that its rotation-equivariant index should be a modular form, closely related to elliptic genera. In this talk we will survey the direct approach to Dirac operators on loop spaces, going from infinite dimensional multilinear algebra and topological foundations to twistor methods and analytic calculations.