Differential geometry, mathematical general relativity, geometric analysis, information geometry.
A common thread in my current work is that probability measures provide a shared language for nonlinear many-particle dynamics and geometric analysis. Alongside this, I continue a program in mathematical relativity on positive mass theorems and rigidity.
Propagation of chaos on Riemannian manifolds. McKean–Vlasov diffusions on manifolds, geometric coupling methods, and uniform-in-time propagation of chaos under curvature hypotheses. Joint work in progress.
Rigidity for the spacetime positive mass theorem with corners. A parallel program in mathematical relativity, continuing recent joint work on the corners setting.
A spacetime positive mass theorem with corners via mollification (With A. F. Wood)
Deterministic-Distance Couplings of Brownian Motions on Radially Isoparametric Manifolds (With G. Cho and T. Kim)
Rigidity of Asymptotically Hyperboloidal Initial Data Sets with Vanishing Mass (With S. Hirsch and Y. Zhang), Commun. Math. Phys. 406, Article 307, 2025
Entropy Stability for Products of Negatively Curved Symmetric Spaces, to appear in Commun. Anal. Geom.
Hyperbolic Mass via Horospheres (with P. Miao), Commun. Contemp. Math. 25 (8), 2250023 (2023)
Scalar curvature deformation and mass rigidity for ALH manifolds with boundary (with L. -H. Huang), Trans. Amer. Math. Soc. 375 (11), 8151-8191, 2022
Some scalar curvature warped product splitting theorems (with G. J. Galloway), Proc. Amer. Math. Soc. 148, 2617-2629 (2020)
Mass rigidity for hyperbolic manifolds (with L. -H. Huang and D. Martin), Commun. Math. Phys. 376, 2329–2349 (2020)
Asymptotically hyperbolic 3-metrics with Ricci flow foliation, Ann. Henri Poincaré 20, 797–811 (2019)
AMS Special Session on Sharp Geometric Inequalities and their Stability, PDEs and Applications
2025 Spring Eastern Sectional Meeting, University of Connecticut, Hartford, CT, Apr 2025
Geometric Analysis Seminar
University of Chicago, Chicago, IL, Apr 2024
Geometric Analysis Seminar
McGill University, Montreal, Canada, Mar 2024
2024 Meeting on Analysis and Noncommutative Geometry for Early Career Researchers
Caltech, Pasadena, CA, Mar 2024
Workshop on Scalar curvature, minimal surfaces, and initial data sets
Harvard CMSA, Cambridge, MA, May 2022
Geometric Analysis Seminar at UM (Virtual)
University of Miami, Miami, FL, Mar 2022
Differential Geometry Seminar at UCSB (Virtual)
University of California, Santa Barbara, Santa Barbara, CA, Nov 2021
Analysis Seminar at OK State University (Virtual)
Oklahoma State University, Stillwater, OK, Oct 2021
Geometry Seminar (Online)
KIAS, Seoul, Korea, Jul 2021
Geometric Analysis and Mathematical Relativity Research Seminar (Online)
University of Tübingen, Tübingen, Germany, Jul 2021
Geometry & Geometric Analysis Seminar (Online)
Clark University, Worcester, MA, Apr 2021 [Video link]
CUNY Geometric Analysis Seminar (Online)
CUNY Graduate Center, New York City, NY, Mar 2021 [Video link]
Geometric Analysis Online Workshop (Online)
Sogang University, Seoul, Korea, Feb 2021
Duke Geometric Analysis and General Relativity Seminar (Online)
Duke University, Durham, NC, Feb 2021
CUNY Geometric Analysis Seminar (Online)
CUNY Graduate Center, New York City, NY, Jul 2020
CMSA General Relativity Seminar (Online)
Harvard CMSA, Cambridge, MA, Apr 2020
Workshop on Geometric Analysis
University of Miami, Miami, FL, Nov 2019
Mathematical Relativity: A Riemannian Approach
CIMAT, Guanajuato, Mexico, May 2019
2019 AMS Spring Eastern Sectional Meeting
University of Connecticut, Hartford, CT, Apr 2019
Analysis learning seminar
University of Connecticut, Storrs, CT, Feb 2019
New York General Relativity Seminar
CUNY Graduate Center, New York City, NY, Nov 2018
Asymptotically Hyperbolic manifolds (18w5108)
Banff International Research Station, Banff, Alberta, Canada, May 2018
Co-organizer, AMS Special Session on Research in Analysis and PDEs by Early Career Mathematicians, 2025 Fall Eastern Virtual Sectional Meeting, October 2025 (with Joshua Flynn and Andrew Miller)
Organizer, Geometry and Topology Seminar, Caltech, 2023–2024
Referee for the Journal of Differential Geometry, the Journal of Geometric Analysis, the Journal of Mathematical Physics, Letters in Mathematical Physics, and the Pacific Journal of Mathematics
Reviewer for Mathematical Reviews (MathSciNet)
Workshop on Scalar curvature, minimal surfaces, and initial data sets
Harvard CMSA, Cambridge, MA, Aug 2020
2020 Virtual Workshop on Ricci and Scalar curvature
Held virtually, Aug 2020
Workshop on Geometric Analysis
University of Miami, Miami, FL, Nov 2019
Mathematical Relativity: A Riemannian Approach
CIMAT, Guanajuato, Mexico, May 2019
A Celebration of Mathematical Relativity in Miami
University of Miami, Miami, FL, Dec 2018
Summer School in Minimal Surfaces, Flows, and Relativity
University of Connecticut, Storrs, CT, Aug 2018
Asymptotically Hyperbolic manifolds (18w5108)
Banff International Research Station, Banff, Alberta, Canada, May 2018
Spring School on Geometric Aspects of General Relativity
Simons Center for Geometry and Physics, Stony Brook, NY, Mar 2018
Geometry and Relativity
Erwin Schrödinger Institute, Vienna, Austria, Jul 2017
Mini-school on Nonlinear Equations
Harvard CMSA, Cambridge, MA, Dec 2016
Aspects of General Relativity
Harvard CMSA, Cambridge, MA, May 2016