- Decoupling theory for various geometric objects in the Euclidean space.
- Maximal operators and local smoothing estimates.
Here are some of the academic articles I have written:
Preprint/Publications:
- Construction of a curved Kakeya set,
with Yue Zhong, (2024),
Link - Two principles of decoupling,
with Jianhui Li, (2024),
Link - A multi-parameter cinematic curvature,
with Mingfeng Chen and Shaoming Guo, (2023),
Link - 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 - Decoupling for smooth surfaces in $\mathbb R^3$, with Jianhui Li (2021), to appear in American Journal of Mathematics:
Link - Decoupling for mixed-homogeneous polynomials in $\mathbb R^3$, with Jianhui Li, Mathematische Annalen, (2021):
Link - Uniform $l^2$ decouping in $\mathbb R^2$ for polynomials, Journal of Geometric Analysis, (2021)
:
Link - On sets containing an affine copy of bounded decreasing sequences, Journal of Fourier Analysis and Applications, (2020)
:
Link
- Kakeya and restriction problems in harmonic analysis (my master thesis, 2017):
Link - Configurations and decoupling: a few problems in Euclidean harmonic analysis (my PhD thesis, 2021):
Link
Notes/Slides:
- Study guide for "On restriction projections to planes in $\mathbb R^3$",
with Tainara Borges and Siddharth Mulherkar, (2024),
Link -
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 ) -
A few remarks on decoupling
(
Link ) -
Equivalence of decoupling constants
(
Link )