I am a postdoctoral researcher at the Technion – Israel Institute of Technology since October 2023, supervised by Dr. Ariel Rapaport. I obtained my Ph.D. degree in June 2023 from Fudan University, under the supervision of Professor Weixiao Shen. I received my B.Sc. degree in June 2018 from Shandong University. 

Research Interests

My primary research interests lie in fractal geometry and dynamical systems.
I am particularly interested in dimension theory within fractal geometry, using tools from dynamical systems, probability, additive combinatorics, random walks, and multiscale analysis.

During my Ph.D., I studied the dimension of strange attractors in smooth dynamical systems, focusing on examples such as the graphs of Weierstrass-type functions and solenoidal attractors.

During my postdoctoral research in Israel, I have worked on dimension problems in iterated function systems, including Bernoulli convolutions and stationary measures associated with Möbius transformations.

More recently, I have developed a growing interest in homogeneous dynamics, geometric group theory, incidence geometry, and geometric measure theory. 

Email: hjren@campus.technion.ac.il   

Publications & Preprints

1. Fourier Decay of SRB Measures for Skew Products, preprint (2026) (with Gaétan Leclerc).

2. Dimension of Bernoulli Convolutions in ℝᵈ, Annals of Probability 54 (2026), no. 4, 2065–2096 (with Ariel Rapaport).

3. Dimension of Furstenberg measures on CP¹, arXiv:2511.00729, (2025) (with Ariel Rapaport).

4. The High-Dimensional Weierstrass Functions, arXiv:2404.06778, submitted, (2024) (with Weixiao Shen).

5. A Dichotomy for the Dimension of Solenoidal Attractors on High-Dimensional Space, Comm. Math. Phys. 405 (2024), no. 5, Paper No. 123, 36 pp.

6. A Dichotomy for the Dimension of SRB Measure, Adv. Math. 442 (2024), Paper No. 109587, 41 pp.

7. Box Dimension of the Graphs of Generalized Weierstrass-Type Functions, Discrete Contin. Dyn. Syst. 43 (2023), no. 10, pp. 3830–3838.

8. A Dichotomy for the Weierstrass-Type Functions, Invent. Math. 226 (2021), no. 3, pp. 1057–1100 (with Weixiao Shen).
   
   

Honors and Awards

Zhong Jiaqing Mathematics Award
Chinese Mathematical Society, 2023

National Scholarship for Graduate Students
Ministry of Education, China, Fall 2019 and Fall 2021
 

Academic Star Grand Prize for Graduate Students
Fudan University, Spring 2022

Selected Talks and Presentations

Fractal Dimension Problems in Dynamical Systems

Shanghai Center for Mathematical Sciences, China, January 15, 2026 

The Fractal Dimension of Graphs of Weierstrass-Type Functions
Summer School on Fractal Geometry, Nanjing University, China, July 2–4, 2025

Geometric Analysis Seminar: Dimension of Furstenberg Measures for SL(2, ℂ) Products
University of Jyväskylä (online), Finland, April 14, 2025

Hausdorff Dimension of Solenoidal Attractors
HUN-REN Alfréd Rényi Institute of Mathematics, Hungary, February 20, 2025

Dimension of Bernoulli Convolutions in ℝᵈ
Geometry of Deterministic and Random Fractals II, Rényi Institute, Hungary, September 2024

Dimension of Furstenberg Measures for SL(2, ℂ) Products
Action Now Seminar, Technion – Israel Institute of Technology, Israel, November 26, 2024

The Hausdorff Dimension of the Graph of Weierstrass-Type Functions
Analysis Seminar, Hunan Normal University, China, August 12–16, 2024

The Dimension of Solenoids
Dynamical Systems Seminar, Institute of Mathematics, Chinese Academy of Sciences, China, September 20, 2023

Academic service: 

referee for Advances in Mathematics，Journal of the London Mathematical Society and for the Journal of Theoretical Probability