Non-negative curvature on exotic spheres

Since their discovery, there has been much interest in the question of precisely which exotic spheres
admit a metric with non-negative sectional curvature. In dimension 7, Gromoll and Meyer found
the first such example. It was subsequently shown by Grove and Ziller that all of the Milnor spheres
admit non-negative curvature. In this talk, it will be demonstrated that the remaining exotic 7-spheres
also admit non-negative curvature. This is joint work with K. Shankar and S. Goette.