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. Marstrand-type projection theorems.

  3. Maximal operators and local smoothing estimates.


Here are some of the academic articles I have written:

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

Preprint/Publications:
  1. A multi-parameter cinematic curvature, with Mingfeng Chen and Shaoming Guo, (2023), Link

  2. A Furstenberg-type problem for circles, and a Kaufman-type restricted projection theorem in $\mathbb R^3$, with Malabika Pramanik and Joshua Zahl, (2022), Link

  3. Decoupling for smooth surfaces in $\mathbb R^3$, with Jianhui Li (2021): Link

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

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

  6. On sets containing an affine copy of bounded decreasing sequences, Journal of Fourier Analysis and Applications, 26(2020), no. 5, 73. MR4150448 : Link


Notes/Slides:
  1. 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)
  2. A few remarks on decoupling (Link)
  3. Equivalence of decoupling constants (Link)