Special interests: differential geometry; geometric analysis; general relativity; partial differential equations
Recent publications: “Localized Deformation for Initial Data Sets with the Dominant Energy Condition.” (Joint with Lan-Hsuan Huang). Calc. Var. Partial Differential Equations. To appear.
“A Note on the Bartnik Mass.” In: L. Bieri, P. T. Chrusciel, S.-T. Yau (eds.), Nonlinear Analysis in Geometry and Applied Mathematics, Harv. Univ. Cent. Math. Sci. Appl. Ser. Math. 1, pp. 49-75 (2017)
“On the P-scalar curvature.” (Joint with Farhan Abedin ’11) J. Geom. Anal. 27, no. 2, 1589-1623 (2017)
“Deformation of Scalar Curvature and Volume.” (Joint with Michael Eichmair and Pengzi Miao) Math. Ann. 357, no. 2, 551-584 (2013)
“Hamiltonian Stationary Tori in Kahler Manifolds.” (Joint with Adrian Butscher). Calc. Var. Partial Differential Equations. 45, no. 1-2, 63-100 (2012).
Honors and Grants:
NSF RUI Grant: 2007-2011, 2012-2015.
Simons Collaboration Grant for Mathematicians, 2011-2012.
Thomas Roy and Lura Forest Jones Lecture Award, Lafayette College, Spring 2011.
Fulbright Fellowship, KTH-Institut Mittag-Leffler, Fall 2008.
NSF Postdoctoral Research Fellowship, Brown University, 2000-2004.
Jon A. Bucsela Prize in Mathematics, MIT, Spring 1994.
Selected courses taught:
Math 264: Differential Equations with Linear Algebra
Math 300: Vector Spaces
Math 312: Partial Differential Equations
Math 343: Advanced Multivariable Calculus
Math 357: Real Analysis II
Math 358: Topology