# Graduate Student / Postdoc Seminar

#### The Positive Mass Theorem and the Intrinsic Flat Distance

Speaker: Dan Lee, CUNY

Location: Warren Weaver Hall 1302

Date: Friday, November 4, 2011, 1 p.m.

Synopsis:

The Schoen-Yau Positive Mass Theorem states that an asymptotically flat 3 manifold with nonnegative scalar curvature has positive ADM mass unless the manifold is Euclidean space. Here we examine sequences of such manifolds whose ADM mass is approaching 0. We assume the sequences have no interior minimal surfaces although we do allow them to have boundary if it is a minimal surface as is assumed in the Penrose inequality. We conjecture that they converge to Euclidean space in the pointed Intrinsic Flat sense for a well chosen sequence of points. The Intrinsic Flat Distance, introduced by Cristina Sormani (CUNY) and Stefan Wenger (UIC), can be estimated using filling manifolds which allow one to control thin wells and small holes. Here we present joint work with Cristina Sormani (CUNY) constructing such filling manifolds explicitly and proving the conjecture in the rotationally symmetric case.