Research Interests
Harmonic analysis is a fascinating branch of mathematics, and is closely related to many other fields that attract me, such as geometric measure theory, geometric function theory, martingale theory, potential theory, and PDEs. Playing with inequalities is what I enjoyed most, especially if they have something to do with the regularity of analytic, geometric, or stochastic objects.
Publications and Preprints
with Zhenbin Cao, Jingyue Li, and Chnagxing Miao, preprint.
2. Sharp restriction estimates for several degenerate higher co-dimensional quadratic surfaces,
with Zhenbin Cao and Changxing Miao, preprint.
3. A study guide for the l^2 decoupling theorem for the paraboloid,
with Ataleshvara Bhargava, Tiklung Chan, and Zi Li Lim, preprint.
4. A short proof of an identity related to Type IV superorthogonality, preprint.
Notes
1. MATH 6440: Partial Differential Equations
2. Notes for the Wave Packet Decomposition, with Chenjian Wang
Slides
1. The proof of the l^2 decoupling conjecture by Bourgain and Demeter, with Ataleshvara Bhargava, Tiklung Chan, and Zi Li Lim.
2. A short proof of an algebraic identity with applications to classical harmonic analysis.