For a summary of my research, here is an old research statement (from 2019). At some point, I'll write a statement for a broader audience, but that's a work in progress. A complete list of publication can be found on my CV (updated June 2023)

My main research focus is geometric analysis, which uses techniques from PDEs to study problems in geometry. Here are some topics which I find interesting.

- Geometric flows (e.g., Ricci flow, curve-shortening flow)
- Spectral geometry
- Optimal transport
- Information geometry
- Geometric probability

### Selected research and exposition

- Log-concavity and fundamental gaps on surfaces of positive curvature, (with Xuan Hien Nguyen, Malik Tuerkoen and Guofang Wei) Submitted. [Arxiv Version]
- Negative curvature constricts the fundamental gap of convex domains (with Xuan Hien Nguyen) Submitted [Arxiv version]
- An illustrated introduction to the Ricci flow (expository paper)
- Kähler-Ricci Flow Preserves Negative Anti-Bisectional Curvature, (with Fangyang Zheng) Submitted. [Arxiv version]
- The Kähler Geometry of Certain Optimal Transport Problems, (with Jun Zhang) Pure and Applied Analysis. [Arxiv version]
- The Set of All Orthogonal Complex Structures on the Flat 6-Tori, (with Bo Yang, and Fangyang Zheng) Adv. Math. [Arxiv version]