I’m a third-year math PhD candidate at MIT, working on problems in differential geometry, geometric analysis, and partial differential equations. My advisor is Prof. William Minicozzi.

I grew up in Hong Kong. Before MIT, I studied at the Australian National University and the University of Melbourne.

Research

1. Drift-harmonic functions with polynomial growth on asymptotically paraboloidal manifolds. Preprint. [arXiv:2501.05119].

Abstract

We construct and classify all polynomial growth solutions to certain drift-harmonic equations on complete manifolds with paraboloidal asymptotics. These encompass the natural drift-harmonic equations on certain steady gradient Ricci solitons. Specifically, we show that all drift-harmonic functions with polynomial growth asymptotically separate variables, and the dimension of the space of drift-harmonic functions with a given polynomial growth rate is finite.

2. Concavity for elliptic and parabolic equations in complex projective space (with Shrey Aryan). Preprint. [arXiv:2403.16783].

Abstract

We establish a concavity principle for solutions to elliptic and parabolic equations on complex projective space, generalizing the results of Langford and Scheuer. To our knowledge, this is the first example of a general concavity principle outside the constant sectional curvature regime, and in particular, our result partially answers a question raised by Korevaar in 1985 regarding the concavity of solutions to elliptic equations on manifolds with non-constant sectional curvature.

3. Positive mass and Dirac operators on weighted manifolds and smooth metric measure spaces (with Isaac M. Lopez and Daniel Santiago). J. Geom. Phys. Vol. 209, No. 105386, 2025. [journal link][arXiv:2312.15441].

Abstract

We show that the weighted positive mass theorem of Baldauf–Ozuch and Chu–Zhu is equivalent to the usual positive mass theorem under suitable regularity, and can be regarded as a positive mass theorem for smooth metric measure spaces. A stronger weighted positive mass theorem is established, unifying and generalizing their results. We also study Dirac operators on certain warped product manifolds associated to smooth metric measure spaces. Applications of this include, among others, an alternative proof for a special case of our positive mass theorem, eigenvalue bounds for the Dirac operator on closed spin manifolds, and a new way to understand the weighted Dirac operator using warped products.

Other writing

1. Uniqueness of tangent flows in mean curvature flow. Undergraduate honours thesis, ANU. Advised by Prof. Ben Andrews.

2. Characteristic classes for the differential geometer. Term paper for Gauge Theory and Symplectic Geometry, ANU.

3. The No Wandering Domains theorem. Term paper for Riemann Surfaces, ANU.

4. Jacobi fields, conjugate points and some applications. Term paper for Differential Geometry, ANU.

5. Topological phases in quantum systems with quantum group symmetries. AMSI VRS research report, Australian Mathematical Sciences Institute/University of Melbourne. Advised by Dr. Thomas Quella.

6. Label-noise robust twin auxiliary classifier GANs. Research report for SCIE30001, University of Melbourne. Advised by Dr. Mingming Gong.