1) "Smooth Convergence Away From Singularities", joint with C. Sormani, Communications in Analysis and Geometry 21, no. 1, 39–104 (2013)

We consider sequences of metrics, g_j , on a compact Riemannian manifold, M, which converge smoothly on compact sets away from a singular set S ⊂ M, to a metric, g_∞ , on M \ S. We prove theorems which describe when M_j = (M, g_j ) converge in the Gromov-Hausdorff (GH) sense to the metric completion, (M_∞ , d_∞ ), of (M \ S, g_∞ ). To obtain these theorems, we study the intrinsic flat limits of the sequences. A new method, we call hemispherical embedding, is applied to obtain explicit estimates on the GH and Intrinsic Flat distances between Riemannian manifolds with diffeomorphic subdomains.