Mathematics of generative modeling and in-context learning
Approximation and statistical capabilities of neural networks
Applications to problems arising from science and engineering, including PDEs, dynamical systems, inverse problems, and optimal transport
A Theory of Diversity for Random Matrices, with Applications to the Task Generalization of Transformers, in collaboration with Yulong Lu. In preparation.
In-Context Operator learning on the Space of Probability Measures, in collaboration with Yineng Chen, Rongjie Lai, Yulong Lu, and Dixi Wang. In preparation.
Provable In-Context Learning of Linear Systems and Linear Elliptic PDEs with Transformers, in collaboration with Yulong Lu, Riley O'Neill, and Tianhao Zhang. Submitted. Arxiv
In-Context Learning of Linear Dynamical Systems with Transformers: Approximation bounds and Depth-Separation, in collaboration with Yulong Lu, Tianhao Zhang, and Yuxuan Zhao. NeurIPS 2025. Arxiv
Score-Based Generative Models Break the Curse of Dimensionality in Learning a Family of Sub-Gaussian Probability Distributions, in collaboration with Yulong Lu. ICLR 2024 Arxiv, poster
Generalization theory for diffusion models, talk at SIAM Conference on Imaging Science (May 2024)
Generalization theory for diffusion models, talk at IMA Data Science Seminar, University of Minnesota (February 2024)
Statistical estimation rates for kernel integral operators, poster at ICERM Workshop on Scientific and Mathematical Machine Learning (June 2023)
Statistical estimation rates for kernel integral operators, contributed talk at Inaugural CAMDA Conference, Texas A&M University (May 2023)
Mathematics of score-based generative modeling, talk at Graduate Student Seminar (GRASS), University of Massachusetts (April 2023)
Introduction to Barron spaces and their generalizations, talk at Learning Learning Seminar, University of Massachusetts (April 2023)
Sampling and the Langevin equation, talk at Graduate Student Seminar (GRASS), University of Massachusetts (November 2022)
Chromatic symmetric functions and the Stanley-Stembridge conjecture, talk at Massachusetts Undergraduate Research Conference (April 2021)
Dynamical systems on complex networks, talk at Undergraduate Math Club, University of Florida (joint talk with Julia Franck) (November 2020)