Geometry & Topology seminar

Jesse Gell-Redman, University of Toronto 

“Index formulas on singular spaces”

Riemannian stratified spaces arise in many contexts, notably as the compactifications of moduli spaces, and on the K ̈ahler-Einstein manifolds studied recently by Donaldson, Tian, and many other. We discuss various extensions of index formulas (such as the Chern-Gauss-Bonnet formula) to these spaces, work which was initiated by Cheeger on manifolds with conical singularities in the 70s. The main object of study are naturally arising elliptic operators (e.g. the Hodge-deRham operator, the Dirac operator) and their mapping properties on these singular spaces. This is joint work with Pierre Albin at UIUC.