Department of Mathematics, Duke University

120 Science Drive, Physics Building

Durham, NC 27708

Email: first name.last name@duke.edu

I am a William W. Elliott Assistant Research Professor in Duke University.

I got my Ph.D in mathematics from the University of Toronto in 2018 under the supervision
of Alex Nabutovsky and Hau-Tieng Wu

My research focuses on establishing the mathematical foundations and application of tools of the massive data analysis. I am also interested in different variational problems in Riemannian geometry.

I apply tools in geometry, mathematical analysis and probability to study the problems in massive data analysis. Especially, I study and develop algorithms in manifold learning.

I use quantitative topology to study different variational problems in differential geometry including closed geodesics and minimal surfaces.

- Diffusion Based Gaussian Process on Restricted Domains

(with David B Dunson, Hau-Tieng Wu), submitted. arXiv:2010.07242 - Strong Uniform Consistency with Rates for Kernel Density Estimators with General Kernels on Manifolds

(with Hau-Tieng Wu), submitted. arXiv:2007.06408 - Data-driven Efficient Solvers and Predictions of Conformational Transitions for Langevin Dynamics on Manifold in High Dimensions

(with Yuan Gao, Jian-Guo Liu), submitted. arXiv:2005.12787 - Spectral Convergence of Graph Laplacian and Heat Kernel Reconstruction in $L^\infty$ from Random Samples

(with David B Dunson, Hau-Tieng Wu), submitted. arXiv:1912.05680 - When Locally Linear Embedding Hits Boundary

(with Hau-Tieng Wu), submitted. arXiv:1811.04423 - Length of a Shortest Closed Geodesic in Manifolds of Dimension Four

(with Zhifei Zhu), accepted by Journal of Differential Geometry. arXiv:1702.07033 - Connecting Dots-from Local Covariance to Empirical Intrinsic Geometry and Locally
Linear Embedding

(with John Malik, Chao Shen, Hau-Tieng Wu), Pure and Applied Analysis, Volume 1 (2019), No. 4, 515-542. - An Upper Bound for the Smallest Area of a Minimal Surface in Manifolds of Dimension
Four

(with Zhifei Zhu), Journal of Geometric Analysis, Volume 30, (2020) 573-600. - Think Globally and Fit Locally Under the Manifold Setup: Asymptotic Analysis of
Locally Linear Embedding

(with Hau-Tieng Wu), Annals of Statistics, Volume 46, Number 6B (2018), 3805-3837.

- 2019 Fall, MATH 212 Multivariable Calculus, Duke University
- 2019 Spring, MATH 212 Multivariable Calculus, Duke University
- 2018 Fall, MATH 212 Multivariable Calculus, Duke University
- 2017 Fall, MAT135 Calculus 1(A) (First year calculus), University of Toronto
- 2016 Summer, MAT235 Calculus II (Multivariable calculus), University of Toronto