My Research Topics
I am interested in harmonic analysis and geometric measure theory. I am currently working on the following topics:


  1. Decoupling theory for various geometric objects in the Euclidean space.

  2. Maximal operators and local smoothing estimates.


Here are some of the academic articles I have written:

Preprint/Publications:
  1. Construction of a curved Kakeya set, with Yue Zhong, (2024), Link

  2. Two principles of decoupling, with Jianhui Li, (2024), Link

  3. A multi-parameter cinematic curvature, with Mingfeng Chen and Shaoming Guo, (2023), Link

  4. A Furstenberg-type problem for circles, and a Kaufman-type restricted projection theorem in $\mathbb R^3$, with Malabika Pramanik and Joshua Zahl, (2022), to appear in American Journal of Mathematics: Link

  5. Decoupling for smooth surfaces in $\mathbb R^3$, with Jianhui Li (2021), to appear in American Journal of Mathematics: Link

  6. Decoupling for mixed-homogeneous polynomials in $\mathbb R^3$, with Jianhui Li, Mathematische Annalen, (2021): Link

  7. Uniform $l^2$ decouping in $\mathbb R^2$ for polynomials, Journal of Geometric Analysis, (2021) : Link

  8. On sets containing an affine copy of bounded decreasing sequences, Journal of Fourier Analysis and Applications, (2020) : Link

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


Notes/Slides:
  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)