Research

Some key words of my research: Fourier restriction estimates, decoupling, local smoothing estimates, maximal operator along curves, cinematic curvature, resolution of singularity, Kakeya, Polynomial method, Hörmander problem, Polynomial Wolff Axioms, kakeya compression, oscillatory integrals, counting rational points near manifold, diophantine approximation.

4.Rational points near planar flat curves

submitted. (arXiv)

3.Oscillatory integral operators and variable Schrödinger propagators: beyond the universal estimates

with Shengwen Gan, Shaoming Guo, Jonathan Hickman, Marina Iliopoulou and James Wright, submitted. (arXiv).  

2.The dichotomy of Nikodym sets and local smoothing estimates for wave equations

with Shaoming Guo, submitted. (arXiv).

1.A multi-parameter cinematic curvature

with Shaoming Guo and Tongou Yang, submitted. (arXiv).

Collaborators

Shengwen Gan, Shaoming Guo, Jonathan Hickman, Marina Iliopoulou, Andreas Seeger, Rajula Srivastava, Niclas Technau, James Wright, Tongou Yang.

Slides and poster

• planar maximal operator(slides)

• The dichotomy of Nikodym sets and local smoothing estimates for wave equations(poster) 

Travel and talks

• 2025/10 AMS Sectional Meeting, “Harmonic Analysis, Geometric Measure Theory and Fractals”, Saint Louis, Missouri. 

• 2025/08 Kopp Summer School: Discrete Directions in Harmonic Analysis, Kopp, Germany.

• 2025/08 Reading and Research Groups in Analysis 2025, University of Pennsylvania, Philadelphia, PA.

• 2025/07 Harmonic Analysis summer school, Chern Institute of mathematics, Nankai university, Tianjin.

• 2025/06 Chern Institute of mathematics, Nankai university, Tianjin.

• 2025/06 Analysis seminar, Capital normal university, Beijing.

• 2025/06 Workshop on Harmonic Analysis and Applications, School of Mathematical Sciences, Peking University.

• 2025/06 Chern Institute of mathematics, Nankai university, Tianjin

• 2025/05 JAMI 2025 The Interplay of Harmonic Analysis, Eigenfunctions of the Laplacian, and Dispersive Partial Differential Equations.

• 2025/04 Analysis seminar, Capital normal university.

• 2025/03 Hot Topics: Interactions between Harmonic Analysis, Homogeneous Dynamics, and Number Theory, SLMath.

• 2025/02 Online Analysis Research Seminar

• 2025/02 Graduate student seminar, UW-Madison, Madison, WI

• 2024/11 Mini course: ''A short proof of l^2 decoupling and its applications'', Westlake univesity, Hangzhou.

• 2024/10 Young scholar in Harmonic analysis, Nanjing university, Nanjing

• 2024/08-2024/12 Chern Institute of mathematics, Nankai university, Tianjin

• 2024/07 Summer school in p-adic harmonic analysis, Nankai university, Tianjin

• 2024/07 Hausdorff School: "Uniformity and Stability of Oscillatory Integrals" and "Maximal Operators and Applications"

• 2024/06 Nanjingxiaozhuang college, Nanjing

• 2024/06 Analysis seminar, Nanjing University, Nanjing

• 2024/05 Analysis seminar, Sun Yat-sen University, Guangzhou

• 2024/05 Madison Lectures in Harmonic Analysis, UW-Madison, Madison, WI

• 2024/04 AMS Sectional Meeting, University of Wisconsin-Milwaukee, Milwaukee, WI

• 2024/04 Graduate student seminar, UW-Madison, Madison, WI

• 2024/03 Graduate Analysis and PDEs Seminar(GAPS), University of Wisconsin-Madison, Madison, WI

• 2024/03 Pittsburgh Links among Analysis and Number Theory(PLANT), University of Pittsburgh and Carnegie Mellon University, Pittsburgh, PA

• 2023/11 UCI fall school:Heat Flow, two-point inequalities, and beyond

• 2023/04 Graduate student seminar, UW-Madison, Madison, WI

• 2022/07 Summer school in harmonic analysis, UW-Madison, Madison, WI