Research

My research interests lie in the areas of Riemannian Geometry, Metric Geometry, and Geometric Measure Theory where I investigate the convergence of spaces under various notions of distance, namely the Gromov- Hausdorff (GH) distance and the Sormani-Wenger intrinsic flat (SWIF) distance. My focus is on manifolds with positive scalar curvature (psc) and the properties which break down for the limiting space under GH- or SWIF-limits.

Papers

Here is a list of my projects.

1. Sequences of Three Dimensional Manifolds with Positive Scalar Curvature (with C. Sormani). Submitted. (Arxiv preprint, Nov 2019)
2. An intrinsic flat limit of Riemannian manifolds with no Geodesics. (with D. Kazaras & C. Sormani). Geometria Dedicata (2019). (Arxiv preprint)
3. Sewing Riemannian Manifolds with Positive Scalar Curvature (with J. Dodziuk and C. Sormani). J. of Geometric Analysis (2017). (Arxiv preprint)
4. Manifold Convergence: Sewing Sequences of Riemannian Manifolds with Positive or Nonnegative Scalar Curvature. PhD Thesis, CUNY Graduate Center (2017).

Select Talks

1. Claremont Colleges Math Colloquiem, October 4, 2017, Claremont Center for the Mathematical Sciences. Title: "Sewing Manifolds with Positive Scalar Curvature."
2. SLC Science Seminar Series, February 14, 2017, Sarah Lawrence College. Title: "Manifold Convergence: Sewing Spaces."
3. CUNY Convergence of Metric Spaces Workshop, August 7-8, 2014, Graduate Center. Title: "Sewing Manifolds with Positive Scalar Curvature."
4. AMS Southeastern Sectional Meeting, March 22, 2014, University of Tennessee, Knoxville. Title: "Sequences of 3D manifolds with psotive scalar curvature."
5. Nonlinear Analysis Seminar, September 27, 2012, CUNY Graduate Center. Title: "Introduction to functions of Bounded-Variation."