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

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

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

  • 2007.12-现在,清华大学数学科学系,教授。

  • 2004-现在,多次访问香港中文大学数学系,合作研究。

  • 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,德国耶拿大学)

学术成果

Selected publications

  1. Jiaxin Hu and Guanhua Liu, Upper estimates of heat kernels for non-local Dirichlet forms on doubling spaces (preprint)

  2. 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 (to appear)

  3. 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.

  4. 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.

  5. 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.

  6. 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.

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

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

  9. 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.

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

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

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

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

  19. 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.


人才培养

至2020年8月,已培养博士毕业生9名(包括1名泰国留学生)、硕士毕业生5名、指导博士后1名,目前在读博士生4名。

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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