My research interests include:
Time-Frequency Analysis of Nonstationary Oscillatory Time Series;
Sparsity and Variable Selections;
Structure-Informed (e.g., group symmetry) Machine Learning: efficient algorithms and theoretical foundations, including finite-sample estimations, uncertainty quantification, and neural network approximation and optimization;
Statistical and Information Divergences and Optimal Transport, their design, associated gradient flows, convergence, and neural network-based algorithms for high-dimensional data and the efficient modeling of rare and extreme events.
Openings:
For prospective PhD students (those with a background in harmonic analysis, probability and stochastic analysis, machine learning or generative modeling, and optimization are particularly welcome), please contact me directly via email with your CV, transcript and a brief description of your research interests. (If you have already been admitted to UNC in math or data science, please send me a list of the math courses you have completed and a brief summary of your research interests.)
I also have openings for postdoctoral positions: please send me your CV and research statement via email.
I will be offering undergraduate research opportunities during Summer 2027. Eligible applicants should be rising seniors at that time, or possess comparable backgrounds in mathematics and programming.
My publications can also be found on my Google Scholar page.
Published Papers:
(with Hyemin Gu, Markos Katsoulakis, Luc Rey-Bellet and Wei Zhu), Robust Generative Learning with Lipschitz-Regularized α-Divergences Allows Minimal Assumptions on Target Distributions. Information and Inference: A Journal of the IMA, Volume 14, Issue 4, December 2025, iaaf028.
(with Markos Katsoulakis, Luc Rey-Bellet and Wei Zhu), Statistical Guarantees of Group-Invariant GANs. SIAM/ASA Journal on Uncertainty Quantification, Vol. 13, Iss. 2 (2025), Pages 862-890.
(with Wei Zhu), On the Implicit Bias of Linear Equivariant Steerable Networks. Thirty-seventh Conference on Neural Information Processing Systems (NeurIPS 2023).
(with Markos Katsoulakis, Luc Rey-Bellet and Wei Zhu), Sample complexity of probability divergences under group symmetry. Fortieth International Conference on Machine Learning (ICML 2023), 4713-4734.
(with Hau-Tieng Wu), Disentangling modes with crossover instantaneous frequencies by synchrosqueezed chirplet transforms, from theory to application. Applied and Computational Harmonic Analysis, Volume 62, January 2023, Pages 84-122.
(with Hau-Tieng Wu), When Ramanujan meets time-frequency analysis in complicated time series analysis. Pure and Applied Analysis 4 (4), 629-673.
(with Yingzhou Li and Xiuyuan Cheng), SpecNet2: Orthogonalization-free spectral embedding by neural networks. The Third Mathematical and Scientific Machine Learning Conference (MSML 2022).
(with Anoopum Gupta, Zhuoqing Chang, Christopher Stephen, Jeremy Schmahmann, Hau-Tieng Wu and Guillermo Sapiro), Accurate Detection of Cerebellar Smooth Pursuit Eye Movement Abnormalities via Mobile Phone Video and Machine Learning. Scientific Reports 10, 18641 (2020).
Preprints:
(with Markos Katsoulakis and Benjamin Zhang), Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences (2026)[arxiv]