Postdoctoral Fellow
Department of Mathematics
The University of Hong Kong
Pokfulam, Hong Kong SAR

Email xxxx@connect.hku.hk, where xxxx = hnwu
Office Room 217, Run Run Shaw Building


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

About

I have been a postdoctoral fellow at the Department of Mathematics, The University of Hong Kong since September 2023, mentored by Prof. Dong Li. Prior to this position, I obtained my PhD degree from the same department 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.

I primarily identify myself as a numerical analyst and an approximation theorist. My research interests lie in the following closely associated areas:
❏ Analysis, partial differential equations (PDEs) and integral equations, and their numerical analysis.
❏ Approximation theory, applied harmonic analysis, and their applications to mathematical data science.

My curriculum vitae.

News

• [Dec. 28, 2023] Our paper "Is hyperinterpolation efficient in the approximation of singular and oscillatory functions?", a joint work with Dr. C. An as well as Chapter 3 of my thesis, has been accepted for publication in the Journal of Approximation Theory.
• [Aug. 09, 2023] Our paper "Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere," a joint work with Dr. C. An as well as Chapter 4 of my thesis, has been accepted for publication in the Journal of Complexity.


• Archived

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
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 selected slides


Restricted isometry and information-based numerical analysis (thesis defense), Department of Mathematics, The University of Hong Kong, Jun 26, 2023.

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 always start my day at the gym, and recently, I started off being a hoppy photographer. I 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.