Non-negative curvature and torus actions

 The classification of Riemannian manifolds with positive and non-negative sectional curvature is a long-standing problem in Riemannian geometry. In this talk I will summarize recent joint work with Catherine Searle on the classification of closed, simply-connected, non-negatively curved Riemannian manifolds admitting an isometric, effective, maximal torus action. This classification has many
applications, in particular the Maximal Symmetry Rank conjecture holds for this class of manifolds.