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Geometric Analysis Seminar

Index-energy estimates for Yang--Mills connections and Einstein metricsĀ 

Casey Kelleher (Princeton)

Location:  Room 705
Date & time: Tuesday, 07 May 2019 at 2:10PM - 3:10PM

Abstract:  We prove a conformally invariant estimate for the index of Schrodinger operators acting on vector bundles over four-manifolds, related to the classical Cwikel-Lieb-Rozenblum estimate. Applied to Yang-Mills connections we obtain a bound for the index in terms of its energy which is conformally invariant, and captures the sharp growth rate. Furthermore we derive an index estimate for Einstein metrics in terms of the topology and the Einstein-Hilbert energy. Lastly we derive conformally invariant estimates for the Betti numbers of an oriented four-manifold with positive scalar curvature.

This is joint work with Matthew Gursky (University of Notre Dame) and Jeffrey Streets (UC Irvine).

Postponed from February 12th

This will be a joint seminar with Geometry/Topology Seminar