范爱华，法国Picardie大学特级教授，武汉大学弘毅客座特聘教授, Wallenberg访问教授 (瑞典隆德大学)。国家高层次人才。范爱华教授于1982年和1985年在武汉大学获得学士和硕士学位，1989年于南巴黎大学（现巴黎萨克雷大学）获得博士学位。发表学术论文120余篇。

研究方向：

动力系统与遍历理论：遍历定理，加权遍历定理，遍历级数、遍历Hilbert变换、Sarnak猜想、Bohr混沌性、遍历优化、Ruelle算子及其应用，非阿基米德动力系统的极小性与混沌性、Lyapounov指数的计算、Furstenberg集合与Furstenberg猜想

随机混沌：随机乘法混沌一般理论、Mandelbrot模型、Gauss混沌、Levy混沌、三角混沌、Dvoretzky覆盖、树上渗流、调和分析中的应用

傅立叶分析：Riesz乘积、缺项三角级数、Hardy函数、Sidon集、扩张级数的收敛性、Fuglede谱猜想、Gelfond指数的计算、Rajchman测度

几何测度论：测度的维数理论、遍历平均与条件变分原理、常返性与熵及维数、加权遍历平均的重分形分析、多重遍历平均的重分形分析

概率论：函数项级数的收敛性、Abel群上平稳过程、行列式点过程、Markov链与随机游动

数论：强一致分布与Khintchin猜想、高维Frobenius问题、动力系统丢番图逼近、连分数与Gauss动力系统、Oppenheim连分数

代表作：

1. Fan, Aihua; Jorg, Schmeling; Weixiao, Shen, Multifractal Analysis of generalized Thue-Morse trigonometric polynomials, Asian J. Math., accepted. https://arxiv.org/abs/2212.13234

2. Fan, Aihua; Klaus Schmidt and Evgeny Verbitskiy, Bohr chaoticity of principal algebraic actions and Riesz product measures, Ergodic Theory Dynam. Systems, Online first, March 6, 2024 https://doi.org/10.1017/etds.2024.13

3. Fan, Aihua; Meyer, Yves, Trigonometric multiplicative chaos and applications to random distributions, Sci. China Math. 66 (2023), no. 1, 3-36. https://doi.org/10.1007/s11425-021-1969-3

4. Fan, Aihua; Fan, Shilei; Ryzhikov, Valery V.; Shen, Weixiao, Bohr chaoticity of topological dynamical systems, Math. Z. 302 (2022), no. 2, 1127-1154. https://doi.org/10.1007/s00209-022-03093-6

5. Fan, Aihua; Herv\'e, Queff\'elec; Martine Queff\'elec, Furstenberg set and its random version, l'Enseignement Math\'ematique, Online first, Nov. 11, 2022 (60 pages). https://ems.press/journals/lem/articles/8188703

6. Fan, Aihua; Karagulyan, Davit, On $\mu$-Dvoretzky random covering of the circle, Bernoulli 27 (2021), no. 2, 1270-1290. https://arxiv.org/abs/1910.08056

7. Fan, Aihua, Multifractal analysis of weighted ergodic averages, Adv. Math. 377 (2021), Paper No. 107488, 34 pp. https://doi.org/10.1016/j.aim.2020.107488

8. Fan, Aihua; Schmeling, Jorg; Shen, Weixiao, $L^\infty$-estimation of generalized Thue-Morse trigonometric polynomials and ergodic maximization, Discrete Contin. Dyn. Syst. 41 (2021), no. 1, 297-327. https://www.aimsciences.org/article/doi/10.3934/dcds.2020363

9. Fan, Aihua; Fan, Shilei; Liao, Lingmin; Shi, Ruxi, Fuglede's conjecture holds in $\mathbb{Q}_p$, Math. Ann. 375 (2019), no. 1-2, 315-341. https://doi.org/10.1007/s00208-019-01867-8

10. Fan, Aihua; Konieczny, Jakub, On uniformity of q-multiplicative sequences, Bull. Lond. Math. Soc. 51 (2019), no. 3, 466-488. https://arxiv.org/abs/1806.04267

11. Fan, Ai-Hua, Weighted Birkhoff ergodic theorem with oscillating weights, Ergodic Theory Dynam. Systems 39 (2019), no. 5, 1275-1289. https://doi.org/10.1017/etds.2017.81

12. Fan, Aihua; Fan, Shilei; Qiu, Yanqi, Some properties of stationary determinantal point processes on ℤ, J. Lond. Math. Soc. (2) 98 (2018), no. 3, 517-535.

13. Fan, Aihua; Schmeling, Jorg, Everywhere divergence of one-sided ergodic Hilbert transform, Ann. Inst. Fourier (Grenoble) 68 (2018), no. 6, 2477–2500.

14. A. H. Fan, J. Schmeling and M. Wu, Multifractal analysis of some multiple ergodic averages. Adv. Math. 295 (2016), 271-333.

15. A. H. Fan, J. Schmeling and S. Troubetzkoy, A multifractal mass transference principle for Gibbs measures with applications to dynamical Diophantine approximation, Proc. London Math. Soc., (3) 107 (2013) 1173–1219.

16. A. H. Fan and L. M. Liao, On minimal decomposition of p-adic polynomial dynamical systems (with L. M. Liao), Advance in Mathematics, 228, no. 4, (2011), 2116-2144.

17. Generic points in systems of specification and Banach valued Birkhoff ergodic average (with L. M. Liao and J. Peyrière), Discrete and Continuous Dynamical Systems Part A, 21 (4)(2008), 1103-1128.

18. A. H. Fan, M. T. Li, J. Y. Yao and D. Zhou, Strict ergodicity of affine p-adic dynamical systems on Z_p , Advances in Math., 214 (2007), 666-700.

19. A. H. Fan and J-P. Kahane, Decomposition principle and random cascades, AMS/IP Stud. Adv. Math., 42, pt, 1,2. American Mathematical Society, Providence, RI, 2008, 447–456.

20. J. Barral and A. H. Fan, Covering numbers of different points in Dvoretzky and Poisson coverings (with J. Barral), Bull. Sci. Math., 129 (2005), no. 4, 275–317.

21. A. H. Fan, D. J. Feng and J. Wu, Recurrence, dimension and entropy, J. London Math. Soc., J. London Math. Soc., 
(2) 64 (2001), 229–244. 


22. A. H. Fan, A proof of the Ruelle operator theorem, Reviews in Math. Phys. Vol.7, No. 8 (1995), 1241– 1247.

23. A. H. Fan , Sur les dimensions de mesures, Studia Math. 111 (1) (1994), 1–17.

24. A.H. Fan, J-P. Kahane, Rareté des intervalles recouvrant un point dans un recouvrement aléatoire, Ann. Inst. Henri Poincaré, 3 (1993), 453–466.

25. A.H. Fan , Equivalence et orthogonalité des mesures aléatoires engendrées par martingales positives homogènes, Studia Math., 98 (3) (1991), 249–266.

26. A. H. Fan, Sur quelques processus de naissance et de mort [On some birth and death processes]. C. R. Acad. Sci. Paris Ser. I. Math. 310 (1990), no.6, 441-444.

27. J. Barral, A. H. Fan and J. Peyriere, Measures generated by multiplication (in French, 153pp), in « Some interactions between analysis, probabilities and fractals» (in French) No. 32, Panorama et Synthèses, SMF, 2010. x+243 pp. [Other authors of the volume: J. Bertoin ,S. Jaffard, J. Berestycki, B. Haas, G. Miermont]

28. 范爱华 Fourier与Fourier分析，pp. 20-64, « 数学所讲座2019»，葛力明、付保华、郑维喆、胡永泉 主编，vii+304, 科学出版社，2023