Christian Bär (UP)
I will explain an eigenvalue estimate for Dirac operators in terms of the hyperspherical radius of the underlying manifold. When combined with other known eigenvalue estimates this has a number of interesting consequences, some of which are known theorems: Llarull's theorem on scalar curvature rigidity, Geroch's conjecture on the nonexistence of positive scalar curvature metrics on tori and a mean value estimate for fill-ins.
