Uwe Semmelmann

Eigenvalue estimates for manifolds with special holonomy

In my talk I will discuss several mostly well-known
results on the kernel and the minimal eigenvalue of the
Laplacian on compact manifolds with special holonomy. The new
point will be the introduction of an operator generalizing
the Laplacian on forms and a general method of producing
Weitzenboeck formulas. My aim is to demonstrate that
these two tools may lead to a better understanding and
hopefully also to new results in the differential
geometry of manifolds with special holonomy.