In case you missed it, here's another link to my research statement.
Articles:
Almost Positive Curvature on the Gromoll-Meyer Sphere: A joint paper with Jost-Hinrich Eschenburg which is to appear in the Proceedings of the American Mathematical Society.
Homogeneous Metrics on Spheres: An expository article published in the Bulletin of the Irish Mathematical Society on my M.Sc. thesis.
Works in progress:
Some new examples with quasi-positive curvature: We describe quotients of by and which admit metrics with quasi-positive curvature.
Curvature on the Eschenburg Spaces: Showing all of the Eschenburg spaces admit quasi-positive curvature, and that the unique cohomogeneity one Eschenburg space not admitting positive curvature admits almost positive curvature.
An infinite family of 4-orbifolds with almost positive curvature: We examine a particular family of 2-torus actions on and show that the resulting quotients all admit almost positive curvature, as long as the action is not free.
Open Problems:
Open problems in non-negative curvature: A list of open problems compiled at the Workshop on Manifolds with Non-Negative Sectional Curvature which was held at AIM, Palo Alto, CA, in September '07.
