Broadly speaking, I am interested in differential geometry and its connection with number theory. More precisely, I study and work on complex manifolds, Riemann surfaces, analytic functions, automorphic functions, invariant metrics, arithmetic differential geometry, and number theory.
- (with A. Buium) Algebraic differential equations satisfied by the K\”ahler-Einstein metrics on punctured Riemann spheres, in progress.
- (with H. N. Huang) $C^1-$estimate for the Calabi flow on toric surfaces, in progress.
- Hyperbolic Metric, Punctured Riemann Sphere and Modular Function. arXiv:1901.06761, DOI: https://doi.org/10.1090/tran/817, Trans. Amer. Math. Soc.
- (with Gunhee Cho) The Kobayashi-Royden metric on punctured spheres. arXiv:1907.07295, DOI:https://doi.org/10.1515/forum-2019-0297, Forum Mathematicum.