English 清华大学 旧版入口 人才招聘

张友金

  • 教授
  • 电话:62771380
  • 邮箱:youjin@tsinghua.edu.cn

基本信息

博士(中国科学技术大学,1994)、教授

工作履历

工作经历

1999.12现在,    清华大学数学科学系,教授

1997.111999.11,日本京都大学数学系,JSPS 博士后

1995.111997.11,意大利国际高等研究院,博士后

1994.011995.10,意大利国际理论物理中心,博士后

1990.061991.07,   俄罗斯斯捷克洛夫数学所圣.彼得堡分所,访问学者

1990.031994.01,中国科学技术大学数学系,助教、讲师

教育经历

1992.021993.10,中国科学技术大学数学系,在职博士研究生

1987.091990.03,中国科学技术大学数学系,硕士研究生

1982.091987.07,中国科学技术大学数学系,本科生



研究领域

数学物理、可积系统理论

所授课程

2023 年春季学期讲授《数学分析 (2)》,2023 年秋季学期讲授《数学分析 (1)》

奖励与荣誉

国家杰出青年基金 (2000

国务院政府特殊津贴 (2006

教育部长江学者特聘教授(2008

教育部自然科学奖一等奖(2018


学术成果

从事数学物理和可积系统理论的研究,包括非线性可积系统的分类、Frobenius 流形及其在 Gromov-Witten 不变量理论中的应用等。发表的主要论文如下:

  1. Variational bihamiltonian cohomologies and integrable hierarchies I: Foundations. Comm. Math. Phys. 401 (2023), 985-1031. (with Si-Qi Liu, Zhe Wang)

  2. The Virasoro-like algebra of a Frobenius manifold. Int. Math. Res. Not. IMRN (2023), 13524-13561. (with Si-Qi Liu, Di Yang, Jian Zhou)

  3. On equivariant Gromov-Witten invariants of resolved conifold with diagonal and anti-diagonal actions. Lett. Math. Phys. 112 (2022), 129. (with Si-Qi Liu, Di Yang, Chunhui Zhou)

  4. Variational bihamiltonian cohomologies and integrable hierarchies II: Virasoro symmetries. Comm. Math. Phys. 395 (2022), 459-519. (with Si-Qi Liu, Zhe Wang)

  5. The loop equation for special cubic Hodge integrals. J. Diff. Geom.121 (2022), 341-368. (with Si-Qi Liu, Di Yang, Chunhui Zhou)

  6. Virasoro constraints for Drinfeld-Sokolov hierarchies and equations of Painlevé type. J. Lond. Math. Soc.(2) 106 (2022), 1443-1500. (with Si-Qi Liu, Chao-Zhong Wu).

  7. Reduction of the 2D Toda hierarchy and linear Hodge integrals. SIGMA Symmetry Integrability Geom. Methods Appl. 18 (2022), 037. (with Si-Qi Liu, Zhe Wang)

  8. Tri-Hamiltonian structure of the Ablowitz-Ladik hierarchy. Phys. D 433 (2022), 133180. (with Shuangxing Li, Si-Qi Liu, Haonan Qu)

  9. The Hodge-FVH correspondence. J. Reine Angew. Math. 775 (2021), 259-300. (with Si-Qi Liu, Di Yang, Chunhui Zhou)

  10. Super tau-covers of bihamiltonian integrable hierarchies. J. Geom. Phys. 170 (2021), 104351. (with Si-Qi Liu, Zhe Wang)

  11. Hodge-GUE correspondence and the discrete KdV equation. Comm. Math. Phys. 379 (2020), 461-490. (with Boris Dubrovin, Si-Qi Liu, Di Yang)

  12. Masur-Veech volumes of quadratic differentials and their asymptotics. J. Geom. Phys. 158 (2020), 103870. (with Di Yang, Don Zagier)

  13. Drinfeld-Sokolov hierarchies and diagram automorphisms of affine Kac-Moody algebras. Comm. Math. Phys. 375 (2020), 785-832. (with Si-Qi Liu, Chao-Zhong Wu, Xu Zhou)

  14. Extended affine Weyl groups of BCD-type: their Frobenius manifolds and Landau-Ginzburg superpotentials. Adv. Math. 351 (2019), 897-946. (with Boris Dubrovin, Ian Strachan, Dafeng Zuo)

  15. Bihamiltonian cohomologies and integrable hierarchies II: the tau structures. Comm. Math. Phys. 361 (2018), 467-524. (with Boris Dubrovin, Si-Qi Liu)

  16. Fractional Volterra hierarchy. Lett. Math. Phys. 108 (2018), 261-283. (with Si-Qi Liu, Chunhui Zhou)

  17. Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs. Adv. Math. 293 (2016), 382-435. (with Boris Dubrovin, Si-Qi Liu, Di Yang)

  18. BCFG Drinfeld-Sokolov hierarchies and FJRW-theory. Invent. Math. 201 (2015), 711-772. (with Si-Qi Liu, Yongbin. Ruan)  

  19. Central invariants of the constrained KP hierarchies. J. Geom. Phys. 97 (2015), 177-189. (with Si-Qi Liu, Xu Zhou)

  20. Proof of a conjecture on the genus two free energy associated to the A_n singularity. J. Geom. Phys. 76 (2014), 10-24. (with Yulong Fu, Si-Qi Liu, Chunhui Zhou)

  21. Uniqueness theorem of W-constraints for simple singularities. Lett. Math. Phys. 103 (2013), 1329-1345. (with Si-Qi Liu, Di Yang)

  22. Bihamiltonian cohomologies and integrable hierarchies I: A special case. Comm. Math. Phys. 324 (2013), 897-935. (with Si-Qi Liu)

  23. On the genus two free energies for semisimple Frobenius manifolds. Russian J. Math. Phys. 19 (2012), 273-298. (with Boris Dubrovin, Si-Qi Liu)

  24. The inversion symmetry of the WDVV equations and tau functions. Physica D 241 (2012), 2168-2177. (with Si-Qi Liu, Dingdian Xu)

  25. Jacobi structures of evolutionary partial differential equations. Adv. Math. 227 (2011), 73-130. (with Si-Qi Liu)

  26. On the Drinfeld-Sokolov hierarchies of D type. Int. Math. Res. Not. IMRN 2011, 1952-1996. (with Si-Qi Liu, Chao-Zhong Wu)

  27. Hamiltonian structures and their reciprocal transformations for the r-KdV-CH hierarchy. J. Geom. Phys. 59 (2009), 1227-1243. (With Ming Chen, Si-Qi Liu)

  28. Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures. Adv. Math. 219 (2008), 780-837. (with Boris Dubrovin, Si-Qi Liu)

  29. On properties of Hamiltonian structures for a class of evolutionary PDEs. Lett. Math. Phys. 84 (2008), 47-63. (with Si-Qi Liu, Chao-Zhong Wu)

  30. Central invariants of semisimple bihamiltonian structures. Proceedings of the 4th International Congress of Chinese Mathematicians III, Higher Education Press, 2008, 380-394.

  31. On quasi-triviality and integrability of a class of scalar evolutionary PDEs. J. Geom. Phys. 57 (2006), 101-119. (with Si-Qi Liu)

  32. A two-component generalization of the Camassa-Holm equation and its solutions. Lett. Math. Phys. 75 (2006), 1-15. (with Ming Chen, Si-Qi Liu)

  33. Bihamiltonian systems of hydrodynamic type and reciprocal transformations. Lett. Math. Phys. 75 (2006), 79-92. (with Ting Xue)

  34. On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasi-triviality of bi-Hamiltonian perturbations. Comm. Pure Appl. Math. 59 (2006), 559-615. (with Boris Dubrovin, Si-Qi Liu)

  35. Deformations of semisimple bihamiltonian structures of hydrodynamic type. J. Geom. Phys. 54 (2005), 427-453. (with Si-Qi Liu)

  36. Virasoro Symmetries of the Extended Toda Hierarchy. Comm. Math. Phys. 250 (2004), 161-193. (with Boris Dubrovin)

  37. The extended Toda hierarchy. Mosc. Math. J. 4 (2004), 313-332. (with Guido Carlet, Boris Dubrovin)

  38. Deformations of the bihamiltonian structures on the loop space of Frobenius manifolds. J. Nonlinear Math. Phys. 9 (2002), Suppl. 1, 243-257.

  39. On the CP^1 topological sigma model and the Toda lattice hierarchy. J. Geom. Phys. 40 (2002), 215-232.

  40. Frobenius manifolds and Virasoro constraints. Selecta Math. (N.S.) 5 (1999), 423-466. (with Boris Dubrovin)

  41. On a reduction of the multi-component KP hierarchy. J. Phys. A 32 (1999), 6461-6476.

  42. Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation. Comm. Math. Phys. 198 (1998), 311-361. (with Boris Dubrovin)

  43. Extended affine Weyl groups and Frobenius manifolds. Compositio Mathematica 111 (1998), 167-219. (with Boris Dubrovin)

  44. On Segal-Wilson's construction for the tau-functions of the constrained KP hierarchies. Lett. Math. Phys. 36 (1996), 1-15.

  45. A remark on the representation theory of the algebra U_q(sl(n)) when q is a root of unity. J. Phys. A 25 (1992), 851-859.


人才培养

指导博士生毕业8名、硕士生毕业3名。其中一位任职清华大学教授,获得国家杰出青年基金;一位任职中国科技大学教授,入选国家青年人才项目;一位任职中山大学教授,获得国家优秀青年基金;一位任职首都师范大学研究员,获得国家优秀青年基金;一位任职南开大学陈省身数学研究所特聘研究员;一位任职澳大利亚墨尔本大学副教授。