Research

I study minimal submanifolds and related topics. Specifically, I am interested in the regularity and fine properties of solutions to geometric PDE and Plateau problems. This work connects nonlinear PDE, the calculus of variations, calibrated geometry, and geometric measure theory. 

Publications & Preprints:

1. Special Lagrangians with multiple isolated singularities (with F. Gaia)
   Submitted. Preprint 2026, arXiv: 2607.26302. [arXiv] [.pdf]

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

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

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

5. 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