郑仕欣

郑仕欣

Postdoc Associate, Department of Mathematics

About me

I am currently a Postdoctoral Associate at the University of Maryland, College Park, working under the mentorship of Professor Haizhao Yang. I earned my Ph.D. in Mathematics from Purdue University, where I was advised by Professor Xiangxiong Zhang.

My research interests lie in computational optimization, with a focus on both the development of efficient algorithms and the analysis of their theoretical guarantees. I am particularly interested in applications across machine learning, data science, partial differential equation (PDE) solvers, and deep learning. Currently, my work centers on analyzing flow-based learning dynamics in deep neural networks.

Professional Experience

  • Postdoctoral Associate, Aug 2025 - Present
    University of Maryland, College Park, MD, USA

Education

  • Ph.D. in Applied Mathematics, Sep 2018 – July 2025
    Purdue University, West Lafayette, IN, USA
    Research Area: Optimization, Riemannian Optimization, Riemannian Sampling, Machine Learning, Eigenvalue Problems

  • B.Sc. in Mathematics and Applied Mathematics, Sep 2014 – May 2018
    Shandong University, Jinan, Shandong, China

Selected Publications & Preprints

  1. S. Zheng, W. Huang, B. Vandereycken, and X. Zhang. Riemannian optimization using three different metrics for Hermitian PSD fixed-rank constraints.
    Journal of Computational Optimization and Applications, 2025.
    Springer link

  2. S. Zheng, H. Yang, and X. Zhang. On the convergence of orthogonalization-free conjugate gradient method for extreme eigenvalues of Hermitian matrices: A Riemannian optimization interpretation.
    Journal of Computational and Applied Mathematics, 451:116053, 2024.
    ScienceDirect link

  3. T. Yu, S. Zheng, J. Lu, G. Menon, and X. Zhang. Riemannian Langevin Monte Carlo schemes for sampling PSD matrices with fixed rank.
    arXiv:2309.04072, 2023. arXiv link

  4. T. Yu, S. Zheng, J. Lu, G. Menon, and X. Zhang. Riemannian Langevin equations for PSD matrices of fixed rank.
    2023 (arXiv available soon).

  5. S. Zheng, J. Lu, X. Zhang. Local convergence of Riemannian gradient descent in solving the ground state of Gross-Pitaevskii eigenvalue problem.
    2024 (arXiv available soon).

  6. S. Zheng, X. Zhang, R. Zhang. Riemannian optimization on stratified sets: convergence of Burer-Monteiro method using a new metric.
    2025 (arXiv available soon).