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Contact Information

Department of Mathematics, Duke University
120 Science Drive, Physics Building
Durham, NC 27708
Email: first name.last name@duke.edu

About Me

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

Research Interest

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.

Papers

  1. Diffusion Based Gaussian Process on Restricted Domains
    (with David B Dunson, Hau-Tieng Wu), submitted. arXiv:2010.07242
  2. Strong Uniform Consistency with Rates for Kernel Density Estimators with General Kernels on Manifolds
    (with Hau-Tieng Wu), submitted. arXiv:2007.06408
  3. 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
  4. 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
  5. When Locally Linear Embedding Hits Boundary
    (with Hau-Tieng Wu), submitted. arXiv:1811.04423
  6. Length of a Shortest Closed Geodesic in Manifolds of Dimension Four
    (with Zhifei Zhu), accepted by Journal of Differential Geometry. arXiv:1702.07033
  7. 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.
  8. 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.
  9. 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.

Teaching

  1. 2019 Fall, MATH 212 Multivariable Calculus, Duke University
  2. 2019 Spring, MATH 212 Multivariable Calculus, Duke University
  3. 2018 Fall, MATH 212 Multivariable Calculus, Duke University
  4. 2017 Fall, MAT135 Calculus 1(A) (First year calculus), University of Toronto
  5. 2016 Summer, MAT235 Calculus II (Multivariable calculus), University of Toronto