Gromov-Hausdorff and Intrinsic Flat Convergence

In this talk we will study sequences of integral current spaces and
metric spaces with boundary. We will prove theorems demonstrating when
the Gromov-Hausdorff and Intrinsic Flat limits of sequences of such
metric spaces agree.  From these theorems we derive compactness theorems
for sequences of oriented Riemannian manifolds with boundary where both
the GH and SWIF limits agree. For these sequences we only require
nonnegative Ricci curvature, upper bounds on volume, noncollapsing
conditions on the interior of the manifold and diameter controls on the
level sets near the boundary.