I am broadly interested in various areas of geometric analysis and have conducted research in the following three areas:
proving the pre-compactness of a sequence of Riemannian manifolds assuming scalar curvature lower bounds,
proving super-convexity of heat kernel in hyperbolic space,
and proving the uniqueness of extremal functions of functional inequality that are conformally invariant.
My research uses tools from geometric measure theory, min-max minimal surface theory, and non-linear PDEs.
More Extreme Limits of Manifolds with Positive Scalar Curvature, arXiv
On the Scalar Curvature Compactness Conjecture in the Conformal Case (Joint with Brian Allen and Changliang Wang), arXiv
Compactness of Sequences of Warped Product Circles over Spheres with Nonnegative Scalar Curvature (Joint with Changliang Wang), accepted for publication in Mathematische Annalen, arXiv
An Extreme Limit with Nonnegative Scalar Curvature (Joint with Christina Sormani and Changliang Wang), accepted for publication in Nonlinear Analysis, arXiv, article
On a family of integral operators on the ball, arXiv
A Compactness Theorem For Rotationally Symmetric Riemannian Manifolds with Positive Scalar Curvature (Joint with Jiewon Park and Changliang Wang) , Pure and Applied Mathematics Quarterly 14(2018), pp 529-561, article, arXiv
Fidelity Approach in Topological Superconductors with Disorders, authors: Wen-Chuan Tian, Guang-Yao Huang, Zhi Wang and Dao-Xin Yao, Physics Letters A, March 2015, article, arXiv
Two-Dimensional Pnictogen Honeycomb Lattice: Structure, On-Site Spin-Orbit Coupling and Spin Polarization, authors: Jason Lee, Wen-Chuan Tian, Wei-Liang Wang and Dao-Xin Yao, Scientific Reports, June 2015, article, arXiv
Geometry and Analysis Seminar, UC Santa Cruz, Nov 2023
Differential Geometry Seminar, UC Santa Barbara, Oct 2023
The 87th Midwest PDE Seminar, University of Notre Dame, May 2023
Geometric and Functional Inequalities and Applications (Remote Talk), Jan 2023
2023 Joint Mathematics Meetings, AMS Special Session on Riemannian Manifolds with Lower Scalar Curvature Bounds II, Boston, Jan 2023
Geometry and Analysis Seminar, UC Santa Cruz, Oct 2022
2022 Joint Mathematics Meetings, AMS Special Session on Intersections of Geometric Analysis and Mathematical Physics (Remote Talk), Apr 2022
Midwest Geometry Conference 2022, Wichita State University, Mar 2022
Tongji University (Remote Talk), Oct 2021
Differential Geometry Seminar, UC Santa Barbara, Oct 2021
SCGP Convergence and Low Regularity in General Relativity, Simon Center, Apr 2019
AMS Sectional Meeting, Special Session on Convergence of Riemannian Manifolds, University of Connecticut Hartford, Apr 2019
CUNY Metric Geometry 2019, CUNY Graduate Center, Jan 2019
McGill University Geometric Analysis Workshop, Jul 2018