English 清华大学 旧版入口 人才招聘
English 清华大学 旧版入口 人才招聘

胡家信

  • 教授
  • 电话： 627 87513
  • 邮箱：hujiaxin@tsinghua.edu.cn
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基本信息

清华大学数学科学系长聘教授、博士（英国圣安德鲁斯大学，2001）

工作履历

  • 2024.06-2024.09，德国比勒菲尔德（Bielefeld）大学, 合作研究。

  • 2023.06-2023.08，德国比勒菲尔德（Bielefeld）大学, 合作研究。

  • 2020.01-2020.02, 加拿大大不列颠哥伦比亚大学（UBC）访问教授。

  • 2019.01-2019.02，日本京都大学访问教授。

  • 2018.01-2018.02, 泰国兰实大学(Rangsit University)访问教授。

  • 2014.05-2014.06，美国康乃尔大学，访问教授。

  • 2008.01-2020.12，多次访问德国比勒菲尔德大学(Bielefeld)，合作研究。

  • 2007-现在，清华大学数学科学系，教授。

  • 2004.01-2020.12，多次访问香港中文大学数学系，合作研究。

  • 2007.07--2007.09,德国耶拿（Jena）大学，洪堡研究学者。

  • 2003.03-2004.07，德国耶拿（Jena）大学，洪堡研究学者。

  • 2001.09-2002.08，香港中文大学，博士后及兼职老师。

  • 1997.11-1998.10，巴黎高等理工大学（Ecole Polytechnique），访问学者。


研究领域

偏微分方程，分形几何，狄氏型理论、热核估计


所授课程

  1. 调和分析引论（研究生）

  2. 概率论与数理统计（本科生）

  3. 线性代数（本科生）

  4. 微积分（本科生）

  5. 几何测度论（研究生）

  6. 分形几何（研究生）

  7. 复分析（研究生）

  8. 概率论（本科生）

  9. 代数与几何（本科生）

  10. 数学专题课（本科生）

奖励与荣誉

德国洪堡学者（2002-03至2003-07，以及2007.07--2007.09，德国耶拿(Jena)大学）

学术成果

Selected publications

  1. A. Grigor'yan, E. Hu, and J. Hu, Tail estimates and off-diagonal upper bounds of the heat kernel, preprint, 2024.

  2. J. Hu and Z. Yu,  Strong elliptic Harnack inequality and heat kernel estimate for the resurrected Dirichlet form, preprint, 2023.

  3. A. Grigor'yan, Eryan Hu and Jiaxin Hu, Parabolic mean value inequality and on-diagonal upper bound of the heat kernel on doubling spaces, Math. Ann. 389 (2024), pp. 2411–2467.

  4. A. Grigor'yan, E. Hu, and J. Hu, Mean value inequality and generalized capacity on doubling spaces, Pure Appl. Funct. Anal., 9 (2024), pp. 111–168.

  5. Falconer, Kenneth J. and Hu, Jiaxin and Zhang, Junda. A dichotomy on the self-similarity of graph-directed attractors, Journal of Fractal Geometry 11 (2024). 161–204.

  6. Hu, Jiaxin and Yu, Zhenyu. The weak eliptic Harnack inequality revisited, Asian J. Math, Special Issue in memory of Professor Ka-Sing Lau, 27 (2023), pp. 771–828.

  7. A. Grigor'yan, Eryan Hu and Jiaxin Hu, Off-diagonal lower estimates and Hölder regularity of the heat kernel, Special Issue in memory of Professor Ka-Sing Lau, 27 (2023), pp. 675–771.

  8. Hu, Jiaxin and Liu, Guanhua. "Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces，Forum Mathematicum, vol. 34, no. 1, 2022, pp. 225-277.

  9. A. Bendikov, A. Grigor'yan, Eryan Hu and Jiaxin Hu, Heat kernels and non-local Dirichlet forms on ultrametric spaces, Annali della Scuola Normale Superiore di Pisa- Classe di Scienze，Vol. XXII (2021), 399-461.

  10. A. Grigor'yan，Eryan Hu and Jiaxin Hu，Two-sided estimates of heat kernels of jump type Dirichlet forms, Adv. Math. 330 (2018), 433-515.

  11. A. Grigor'yan，Eryan Hu and Jiaxin Hu，Lower estimates of heat kernels for non-local Dirichlet forms on metric measure spaces, J. Funct. Anal. 272 (2017), 3311–3346.

  12. A. Grigor'yan，Jiaxin Hu and Ka-Sing Lau，Generalized capacity, Harnack inequality and heat kernels of Dirichlet forms on metric measure spaces, J. Math. Soc. Japan, 67 (2015), 1485-1549.

  13. A. Grigor'yan，Jiaxin Hu and Ka-Sing Lau，Estimates of heat kernels for non-local regular Dirichlet forms, Trans. Amer. Math. Soc. 366 (2014), 6397-6441.

  14. A. Grigor'yan，Jiaxin Hu, Upper bounds of heat kernels on doubling spaces, Moscow Math. J. 14 (2014), No. 3, 505-563.

  15. A. Grigor'yan，Jiaxin Hu, Heat kernels and Green functions on metric measure spaces, Canadian J. Math. 66 (2014), 641-699.

  16. A. Grigor'yan, J. Hu and K.-S. Lau, Comparison inequalities for heat semigroups and heat kernels on metric measure spaces, J. Funct. Anal. 259 (2010), 2613-2641.

  17. Jiaxin Hu and Martina Zähle:  Generalized Bessel and Riesz potentials on metric measure spaces, Potential Anal. 30 (2009), 315-340.

  18. A. Grigor’yan and Jiaxin Hu: Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces, Inventiones Mathematicae 174 (2008), 81-126.

  19. A. Grigor’yan; Jiaxin Hu and Ka-Sing Lau: Obtaining upper bounds of heat kernels from lower bounds, Comm. Pure Appl. Math. 61 (2008), no. 5, 639-660.

  20. Jiaxin Hu and X.P. Huang, A note on the limiting weak-type behavior for maximal operators, Proc. Amer. Math. Soc. 136 (2008), 1599-1607.

  21. A. Grigor’yan, Jiaxin Hu and Ka-Sing Lau: Equivalence conditions for on-diagonal upper bounds of heat kernels on self-similar spaces, J. Funct. Anal. 237 (2006), 427-445.

  22. Jiaxin Hu, K.-S. Lau and S.-M. Ngai: Laplace operators related to self-similar measures on Rd, J. Funct. Anal. 239 (2006), 542-565.

  23. A. Grigor’yan, Jiaxin Hu and Ka-Sing Lau: Heat kernels on metric-measure spaces and an application to semi-linear elliptic equations, Trans. Amer. Math. Soc. 355 (2003), 2065--2095.

  24. Kenneth J. Falconer and Jiaxin Hu: Nonlinear diffusion equations on unbounded fractal domains. J. Math. Anal. Appl. 256 (2001), 606–624.

  25. Jiaxin Hu and P.G. LeFloch: L1-continuous dependence property for systems of conservation laws, Arch. Rational Mech. Anal. 151 (2000), 45-93.

  26. Jiaxin Hu: The Riemann problem for pressureless fluid dynamics with distribution solutions in Colombeau’s sense, Comm. Math. Phys, 194 (1998), 191-205.

  • Book： 《分形分析引论》，胡家信著，科学出版社，2013，230页。An introduction to fractal analysis (in Chinese, 230 pages), Science Press, 2013.


参加国际会议信息

  1. "Fractal Geometry"，July 3-7, 2023, Edinburgh, UK.

  2. International Conference on Fractal Geometry and Related Topics, Hong Kong （December 11-15, 2023）

  3. "Smooth Functions on Rough Spaces and Fractals with Connections to Curvature Functional Inequalities", November 20--25, 2022, Banff International Research Station (BIRS), Canada (online).

  4. CIRM Conference "Nonlinear Elliptic and Parabolic PDEs", Levico Terme (Trento), Oct. 11-15, 2021 (online).

  5. Master Lectures--the Legacy of of Carl Friedrich Gauss (December 18- 22 , 2017, Sanya, China).

  6. Heat kernels and Analysis on Manifolds and Fractals (July 11- 16, 2016, Germany).

  7. The 5th Cornell Conference on Analysis, Probability, and Mathematical Physics on Fractals (June 11-15, 2014, Cornell University, USA).

  8. Conference in honour of Kenneth Falconer's 60th birthday (May 12-14, 2014, Paris, France).

  9. The 6th International Congress of Chinese Mathematicians (July 13-19, 2013, Taipei, Taiwan).

  10. 2013 NCTS Workshop on Dynamical Systems(July 22-24, 2013, Hsinchu, Taiwan).

  11. Workshop on Fractal Geometry and Related Topics (May 4-5, 2012, Hong Kong).

  12. Workshop Curvature measures and Integral Geometry (March 1-3, 2012, Prague, Czech Republic).

  13. Stochastic and Real World Models 2011 (July 18-21, 2011. Bielefeld, Germany)

  14. The 5th International Congress of Chinese Mathematicians (Dec 17-22, 2010, Beijing, China).

  15. International Conference: Fractal Geometry and Stochastics 4 (Sept 8-12, 2008, Greifswald, Germany).

  16. Geometric Measure Theoretic Approaches to Potentials on Fractals and Manifolds (April 8-14, 2007. MFO,Germany).

相关网址：mathscinet, arXiv, MathSciDoc, mathgenealogy, MacTutor History


人才培养

至2023年9月，已培养博士毕业生12名（包括1名泰国留学生）、硕士毕业生5名、指导博士后1名。

  1. Zhenyu Yu, Lecturer at National University of Defense Technology of China (Initial employer after graduation) (July 2023)

  2. Junda Zhang, Postdoc, South China University of Technology (Initial employer after graduation) (July 2023).

  3. Guanhua Liu, Postdoc, University of Bielefeld, Germany (Initial employer after graduation) (July 2022)

  4. Jin Gao Lecturer at Hangzhou Normal University, China (Initial employer after graduation) (July 2020).

  5. Meng Yang, University of Bielefeld, Germany (Initial employer after graduation) (January 2018).

  6. Hongwei Bao, Postdoc (September, 2017), Ningbo University (Initial employer after graduation)

  7. Xuliang Li, Watrix Technology (Beijing) (Initial employer after graduation) (PhD, 2017).

  8. Chaoyi Zhu, Ubiquant Investment (Beijing) (Initial employer after graduation) (Master, 2017).

  9. Pichit Boonkrong, Thailand, Lecturer at Rangsit University (Initial employer after graduation) (PhD, 2016).

  10. Xiaoman Dou, Postdoc, Bosera Funds, Shenzhen, China (Initial employer after graduation) (PhD, 2015)

  11. Qingsong Gu, Postdoc, The Chinese University of Hong Kong (Initial employer after graduation) (PhD, 2015).

  12. XiaoXiang Chai, PhD student, The Chinese University of Hong Kong (Initial employer after graduation) (Master, 2015).

  13. Song Huang, Guangzhou Securities, Guangzhou, China (Initial employer after graduation) (Master, 2015).

  14. Eryan Hu, Postdoc, Beijing Institute of Technology, China (Initial employer after graduation) (PhD, 2013).

  15. Yuhua Sun, University of Bielefeld, Germany (Initial employer after graduation) (2012).

  16. Xueping Huang, PhD student, University of Bielefeld, Germany (Initial employer after graduation) (Master, 2008).

  17. X.S. Wang, PhD student, University of Glasgow, Scotland, UK (Initial employer after graduation) (Master, 2006).

  18. Yuan Ji, China Everbright Bank, China (Initial employer after graduation) (PhD, 2006, Joint Supervisor).