B3 Moduli spaces of metrics of positive curvature

In this project, the space of Riemannian metrics of positive scalar curvature on closed manifolds will be studied. Central research questions concern the nontriviality of secondary index invariants, rigidity theorems for the homotopy type of those spaces and the action of the diffeomorphism group, and the comparison of two iterated loop space structures. We will use techniques from differential geometry, higher index theory, metric geometry, differential topology and homotopy theory.