Geometric Analysis Seminar: Stephen McKeown (UT Dallas)

Title: Self-dual and even Poincaré-Einstein metrics in Dimension Four 

Abstract: One of the most important invariants Poincaré-Einstein metrics is their renormalized volume, yet it is a subtle quantity. We present rigidity and gap theorems for the renormalized volume of self-dual and even Poincaré-Einstien metrics in dimension four. As a corollary, we give an obstruction to the existence of self-dual Poincaré-Einstein metrics in terms of conformal invariants of the boundary and the topology of the bulk.