Mathematics

 In this talk I will summarize joint work with Wolfgang Ziller.  In contrast to the positive curvature setting, there exist comparatively many examples with non-negative sectional curvature.  Hence it is natural to ask whether, among the known examples,  it is possible to topologically distinguish manifolds with non-negative curvature from those admitting positive curvature.  We study the topology of various sphere bundles over CP^2 which admit a metric of non-negative sectional curvature.  We then compare their diffeomorphism types with known examples of positively curved manifolds.  I will also discuss a recent simplification of the homeomorphism invariants of such manifolds obtained jointly with Pongdate Montagantirud.