New methods in spectral geometry.

The projects uses methods from mathematical scattering theory to resolve some outstanding problems in thespectral analysis and index theory of differential operators. These problems have been raised by eminentphysicists such as E. Witten as well as mathematicians working on famous conjectures in differential geometry.The resolution of these problems will also have an impact on non-commutative analysis. The project's results willapply to theoretical models of quantum phenomena whose spectral properties are at the limit of the range ofcontemporary mathematical techniques.