- Decoupling theory for various geometric objects in the Euclidean space.
- Marstrand-type projection theorems.
- Maximal operators and local smoothing estimates.
Here are some of the academic articles I have written:
Theses:
- 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
- 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),
Link
- Decoupling for smooth surfaces in $\mathbb R^3$, with Jianhui Li (2021):
Link
- Decoupling for mixed-homogeneous polynomials in $\mathbb R^3$, with Jianhui Li, (2021), Mathematische Annalen:
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, 26(2020), no. 5, 73. MR4150448 :
Link
Notes/Slides:-
A Study Guide for A Study Guide for the l^2 decoupling Theorem by Bourgain and Demeter (2016)
(
) and (Link to [Bourgain-Demeter] )Link to my note -
A few remarks on decoupling
(
)Link -
Equivalence of decoupling constants
(
)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),