Postdoctoral Research and Teaching Associate
Department of Mathematics
University of Georgia
Athens, GA 30602

Email xxxx@uga.edu (working) and xxxx@connect.hku.hk (permanent), where xxxx = hnwu
Office 627A Boyd Research and Education Center
Office hours Nil in Spring 2025


Photo by Yanning Chen (HKU Main Building, Dec 2023)
(More Photos)

About

I have been a postdoctoral associate at the Department of Mathematics, University of Georgia since August 2024, working with Prof. Weiwei Hu. Prior to this position, I was a postdoctoral fellow at the Department of Mathematics, University of Hong Kong, mentored by Prof. Dong Li. I obtained my PhD degree from the University of Hong Kong in 2023, under the supervision of Prof. Xiaoming Yuan, and completed my BSc degree at Jinan University, Guangzhou, China in June 2019, both in mathematics.

My primary research focus is on constructive approximation approaches for problems of continuous mathematics involving functions, equations, and controls. Broadly in analysis and applied mathematics, my research areas lie in the following closely related fields:

❏ Approximation theory, applied harmonic analysis, and their applications to mathematical data science.
❏ Partial differential equations (PDEs), integral equations, and their numerical analysis.
❏ Optimization and optimal control for dynamical systems governed by PDEs.

My curriculum vitae.

News

• [Nov. 25, 2024] New preprint: Marcinkiewicz--Zygmund inequalities for scattered data on polygons.


• Archived

Travel Plans

• NASHVILLE, TN, United States (May 19-22, 2025) — Shanks Conference 2025, Vanderbilt University
• AUBURN, AL, United States (Apr 4-5, 2025) — Southeast Applied and Computational Math Student Workshop, Auburn University
• ATLANTA, GA, United States (Feb 8, 2025) — 2025 Georgia Scientific Computing Symposium, Georgia Institute of Technology


• Past Travels

Research Repository

See my publications and codes in the databases above or the full list below (click to open):

Complete list of publications


Not yet appeared
Marcinkiewicz--Zygmund inequalities for scattered data on polygons.
Preprint. arXiv:2411.16584

Spherical configurations and quadrature methods for integral equations of the second kind, with C. An.
Preprint. arXiv: 2408.14392

Breaking quadrature exactness: A spectral method for the Allen--Cahn equation on spheres, with X. Yuan.
Preprint. arXiv: 2305.04820


2024
Is hyperinterpolation efficient in the approximation of singular and oscillatory functions?, with C. An.
J. Approx. Theory, 299 (2024), 106013. arXiv: 2205.08218
Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere, with C. An.
J. Complexity, 80 (2024), 101789. arXiv: 2209.11012.

2023
Restricted isometry and information-based numerical analysis.
PhD Thesis (2023). The University of Hong Kong. HKU Theses Online.
Enhanced total variation minimization for stable image reconstruction, with C. An and X. Yuan.
Inverse Probl., 39 (2023), 075005. arXiv: 2201.02979.

2022
On the quadrature exactness in hyperinterpolation, with C. An.
BIT Numer. Math., 62 (2022), 1899-1919. arXiv: 2202.13691.
The springback penalty for robust signal recovery, with C. An and X. Yuan. 
Appl. Comput. Harmon. Anal., 61 (2022), 319-346. arXiv: 2110.06754.  

2021
Lasso hyperinterpolation over general regions, with C. An.
SIAM J. Sci. Comput., 43 (2021), A3967–A3991. arXiv: 2011.00433.
Tikhonov regularization for polynomial approximation problems in Gauss quadrature points, with C. An.
Inverse Probl., 37 (2021), 015008. arXiv: 2008.00899.

Collection of slides


Hyperinterpolation, Marcinkiewicz-Zygmund property, and their use for *integral equations*, Applied Math Seminar, University of Georgia, Oct 15, 2024.
Hyperinterpolation, Marcinkiewicz-Zygmund property, and their use for *spectral methods*, International Conference on Analysis and Applications (ICAA 2024) in honor of Roderick S. C. Wong’s 80th birthday, City University of Hong Kong, Jun 4, 2024.
Restricted isometry and information-based numerical analysis (thesis defense), Department of Mathematics, The University of Hong Kong, Jun 26, 2023.

Here is a word cloud generated from the text data of my research articles using the Text Analytics Toolbox in MATLAB (Sept 2024)

More about Me

Every Chinese name carries a specific and unique meaning, and mine is no exception. Hao (浩) signifies "vast and torrential water," while Ning (宁) represents "to pacify and stabilize." Thus, my name, Hao-Ning, depicts a scene where mighty water finally finds serenity.

I am originally from Wanxian, Sichuan (now Wanzhou district, Chongqing), a city nestled on the banks of the Yangtze River in southwestern China and situated at the easternmost point of the Sichuan Basin. The upper Yangtze River alters her course from northeast to due east here, and soon after, she carves a passage through the majestic mountains at the eastern edge of the basin, famously known as the Three Gorges.

I love exploring the world and am also an avid museum enthusiast, particularly drawn to museums dedicated to natural and human history. Yet, I find little appeal in the realm of postmodern art.

GUANGZHOU, China (June 4, 2019) — I appreciate the mathematical convention of authorship order that Hardy and Littlewood made famous: the authors are alphabetically ordered and everyone gets an equal share of credit. If I have the privilege of working with you, I would be honored to adhere to this tradition.

My Erdős number is 5:
❏ Paul Erdős - George G. Lorentz - Sherman D. Riemenschneider - Raymond H. Chan - Xiaoming Yuan - W.
❏ Paul Erdős - Ralph Philip Boas Jr. - Philip M. Anselone - Ian H. Sloan - Congpei An - W.

Last Modified: Jan 26, 2025 - Athens, GA