## about me

I am an associate professor in the Department of Mathematics at Union College. Previously, I was a Hans Rademacher Instructor of Mathematics at the University of Pennsylvania. I received my Ph.D. in 2010 from Duke University under the direction of Hubert Bray. Prior to that, I received my bachelor's degree from Harvey Mudd College. Here is my CV.

## teaching

Here are archives of my course webpages from UPenn.

## research

**primary interests:**

*geometric analysis, mathematical relativity*I work in geometric analysis, emphasizing connections with general relativity. Einstein's theory of general relativity describes the universe as a spacetime, which is a four-dimensional continuum containing all points and events, past, present and future. Gravitational effects (for instance, due to a black hole) manifest through the curvature of spacetime, and thus geometry plays an important role in the theory. My research typically involves scalar curvature and explores connections between mass and geometry, including "quasi-local" mass and the total "ADM" mass of a spacetime. My current interests include convergence of sequences of asymptotically flat manifolds, Bartnik's quasi-local mass conjectures, and understanding mass in low regularity settings.

## papers

Note: links below are to preprints, not final versions.

*Proc. Amer. Math. Soc.*, Vol. 149, No. 11 (2021).

*Comm. Anal. Geom.*

*Calc. Var. Partial Differential Equations*, Vol. 60, No. 2 (2021).

*Journal of Geometry and Physics*, Vol. 136 (2019), pp. 228-243.

*Pacific Journal of Mathematics*, Vol. 301, No. 2 (2019), pp. 441-466.

*Annales Henri Poincaré*, Vol. 20, No. 5 (2019), pp. 1651-1698.

*Journal für die reine und angewandte Mathemtik*(Crelle' s Journal), Vol. 76 (2019), pp 227-257.

*Communications in Analysis and Geometry*, Vol. 26, No. 1 (2018), pp. 85-111.

*Annals of Global Analysis and Geometry*, Vol. 54, No. 4 (2018), pp. 509-527.

*Annales Henri Poincaré*, Vol. 17, No. 6 (2016) pp. 1457-1475.

*Archiv der Mathematik*., Vol. 104, No. 6 (2015), pp. 561-575.

*Journal of Geometric Analysis*, Vol. 25, No. 1 (2015), pp. 668-708.

*Communications in Mathematical Physics*, Vol. 335, No. 1 (2015), pp. 285-307.

^{**}, C. Fenton, C. Chee, A.G.C. Bergqvist) Epilepsy Treatment Simplified through Mobile Ketogenic Diet Planning,

*Journal of Mobile Technology in Medicine*, Vol. 3, No. 2 (2014).

*Classical and Quantum Gravity*30 (2013) 195007. Chosen for inclusion in IOP Select.

*Pacific Journal of Mathematics*, Vol. 261, No. 2 (2013), pp. 417-444.

*Communications in Analysis and Geometry*, Vol. 20, No. 1 (2012), pp. 163-202.

*Asian Journal of Mathematics*, Vol. 17 No. 3 (2013).

^{**}denotes undergraduate coauthor

## notes

Below are expository notes I have written on a variety of topics. Comments are always welcome.

## mathematical reviews

Here is a link to review articles I have written for Mathematical Reviews. (MathSciNet access required)