I am currently working on the following topics:

1. Decoupling theory for various geometric objects in the Euclidean space.
2. Curved Kakeya problems and their related maximal operators.

Theses:

1. Kakeya and restriction problems in harmonic analysis (my master thesis, 2017): Link
2. Configurations and decoupling: a few problems in Euclidean harmonic analysis (my PhD thesis, 2021): Link

1. Study guide for "On restriction projections to planes in $\mathbb R^3$", with Tainara Borges and Siddharth Mulherkar, (2024), Link
2. A Study Guide for A Study Guide for the l^2 decoupling Theorem by Bourgain and Demeter (2016) (Link to [Bourgain-Demeter]) and (Link to my note)
3. A few remarks on decoupling (Link)
4. Equivalence of decoupling constants (Link)

I am teaching MA127 (Calculus II) in Fall 2025 at SUSTech. Below are courses I have previously taught elsewhere (some courses were taught more than once):

1. Linear Algebra and Applications (MATH 33A) UCLA 2025
2. Differential Geometry (MATH 120A) UCLA 2025
3. Complex Analysis for Applications (MATH 132) UCLA 2025
4. Linear Algebra and Applications (MATH 33A) UCLA 2024
5. Linear Algebra and Applications (MATH 33A) UCLA 2024
6. Complex Analysis for Applications (MATH 132) UCLA 2023
7. Elementary Topology (MATH 551) UW-Madison 2023
8. Analysis I (MATH 521) UW-Madison 2022
9. Introduction to Complex Variables (MATH 300) UBC 2022
10. Integral Calculus with Applications to Commerce and Social Sciences (MATH 105) UBC 2019
    
    
    
    
    
    
    
    
    
    

Publications:

1. (Joint with Yue Zhong) Construction of a curved Kakeya set, Bulletin of the London Mathematical Society, 2025, https://doi.org/10.1112/blms.70110
2. (Joint with Malabika Pramanik and Joshua Zahl) A Kaufman type restricted projection theorem in R3 (2022), and a Kaufman-type restricted projection theorem in R^3, accepted by American Journal of Mathematics in 2024, arXiv:2207.02259
3. (Joint with Jianhui Li) Decoupling for smooth surfaces in R3 (2021), accepted by American Journal of Mathematics in 2023, arxiv:2110.08441
4. (Joint with Jianhui Li) Decoupling for mixed-homogeneous polynomials in R3. Mathematische Annalen, 2022, https://link.springer.com/article/10.1007/s00208-021-02273-9
5. Uniform l2-decoupling in R2 for polynomials. Journal of Geometric Analysis, 2021, https://doi.org/10.1007/s12220-021-00666-5
6. On sets containing an affine copy of bounded decreasing sequences. Journal of Fourier Analysis and Applications, 2020, https://doi.org/10.1007/s00041-020-09780-4.

Preprints:

1. (Joint with Jianhui Li) Decoupling for degenerate hypersurfaces (2025), arxiv:2507.02134
2. (Joint with Jianhui Li) Decoupling for surfaces with radial symmetry (2025), arxiv:2504.17100
3. (Joint with Xianghong Chen and Yue Zhong) Improved packing of hypersurfaces in Rd (2025), arxiv:2501.03532
4. (Joint with Jianhui Li) Two principles of decoupling (2024), arxiv:2407.16108
5. (Joint with Mingfeng Chen and Shaoming Guo) A multi-parameter cinematic curvature (2023), arxiv:2306.01606