Research

I work in geometric analysis and nonlinear PDE, focusing on high-codimension minimal submanifolds as a model for understanding the structure of elliptic systems (and vice versa). My research develops geometric and analytic methods to study singularity formation, regularity, existence, and uniqueness in regimes where scalar techniques break down. This work connects geometric PDE, the calculus of variations, calibrated geometry, and geometric measure theory. 

Publications & Preprints:

1. Uniqueness in the Plateau problem for calibrated currents (with C.-K. Lee)
   Submitted. Preprint 2025, arXiv: 2510.02299. [arXiv] [.pdf]

2. Minimal submanifolds with multiple isolated singularities
   Submitted. Preprint 2024, arXiv: 2409.20327. [arXiv] [.pdf] [slides]

3. Strict stability of calibrated cones (with J. Lee)
   Proc. Amer. Math. Soc. 153 (2025), 4411-4422. [journal] [arXiv] [.pdf]

4. Partial regularity for Lipschitz solutions to the minimal surface system
   Calc. Var. PDE 60 (2023), no. 260. [journal] [arXiv] [.pdf] [slides]

Theses:

1. Ph.D. Thesis, UC Irvine [.pdf] [slides]
   Title: On the existence, uniqueness, and regularity theory for minimal submanifolds with high codimension

2. M.S. Thesis, UT San Antonio [.pdf]
   Title:  De Giorgi's conjecture for the Allen-Cahn equation and related problems for classical and fractional Laplacians