Email: youjin@tsinghua.edu.cn

 

教育背景

博士(中国科学技术大学,1994年)、教授(博导)

工作履历

1999.12–现在,清华大学数学科学系,教授

1997.11–1999.11,日本京都大学数学系,JSPS博士后

1995.11–1997.10,意大利国际高等研究院,博士后

1994.01–1995.10,国际理论物理中心,博士后

1990.06–1991.07,俄罗斯斯捷克洛夫数学所圣.彼得堡分所,访问学者

1990.03–1994.01,中国科学技术大学数学系,助教、讲师

研究领域

数学物理、可积系统理论。

 

奖励与荣誉

国家杰出青年基金、教育部自然科学奖一等奖获得者,教育部长江学者特聘教授。

学术成果

主要从事数学物理和可积系统理论的研究,与合作者在非线性可积系统的分类理论、Frobenius流形理论及其在Gromov-Witten不变量理论中的应用等方面作出了一系列重要的工作。代表性论文如下:

1. Drinfeld-Sokolov hierarchies and diagram automorphisms of affine Kac-Moody algebras. To appear in Communications in Mathematical Physics. (with S.-Q. Liu, C.-Z. Wu, X. Zhou)

2. Extended affine Weyl groups of BCD-type: their Frobenius manifolds and Landau-Ginzburg superpotentials, Advances in Mathematics 351 (2019), 897-946. (with B. Dubrovin, I. Strachan, D. Zuo).

3. Bihamiltonian cohomologies and integrable hierarchies II: the tau structures. Communications in Mathematical Physics 361 (2018), 467-524. (with B. Dubrovin, S.-Q. Liu)

4. Fractional Volterra hierarchy. Letters in Mathematical Physics 108 (2018), 261-283. (with S.-Q. Liu, C. Zhou)

5. Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs.  Advances in Mathematics 293 (2016), 382-435. (with B. Dubrovin, S.-Q. Liu, D. Yang)

6. BCFG Drinfeld-Sokolov hierarchies and FJRW-theory. Inventiones Mathematicae 201 (2015), 711-772. (with S.-Q. Liu, Y. Ruan) 

7. Proof of a conjecture on the genus two free energy associated to the A_n singularity. Journal of Geometry and Physics 76 (2014), 10-24. (with Y. Fu, S.-Q. Liu, C. Zhou)

8. Bihamiltonian cohomologies and integrable hierarchies I: a special case. Communications in Mathematical Physics 324 (2013), 897-935. (with S.-Q. Liu)

9. Uniqueness theorem of W-constraints for simple singularities. Letters in Mathematical Physics 103 (2013), 1329-1345. (with S.-Q. Liu, D. Yang)

10. On the genus two free energies for semisimple Frobenius manifolds. Russian Journal of Mathematical Physics 19 (2012), 273-298. (with B. Dubrovin, S.-Q. Liu)

11. The inversion symmetry of the WDVV equations and tau functions. Physica D 241 (2012), 2168-2177. (with S.-Q. Liu, D. Xu)

12. Jacobi structures of evolutionary partial differential equations, Advances in Mathematics 227 (2011), 73-130. (with S.-Q. Liu)

13. On the Drinfeld-Sokolov hierarchies of D type. International Mathematics Research Notices 2011 (2011), 1952-1996. (with S.-Q. Liu, C.-Z. Wu)

14. Hamiltonian structures and their reciprocal transformations for the r-KdV-CH hierarchy. Journal of Geometry and Physics 59 (2009), 1227-1243. (with M. Chen, S.-Q. Liu)

15. Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures, Advances in Mathematics 219 (2008), 780-837. (with B. Dubrovin, S.-Q. Liu)

16. On properties of Hamiltonian structures for a class of evolutionary PDEs. Letters in Mathematical Physics 84 (2008), 47-63. (with S.-Q. Liu, C.-Z. Wu)

17. On Hamiltonian perturbations of hyperbolic systems of conservation laws I: quasi-triviality of bi-Hamiltonian perturbations. Communications on Pure and Applied Mathematics 59 (2006), 559-615. (with B. Dubrovin, S.-Q. Liu)

18. A two-component generalization of the Camassa-Holm equation and its solutions. Letters in Mathematical Physics 75 (2006), 1-15. (with M. Chen, S.-Q. Liu)

19. On quasi-triviality and integrability of a class of scalar evolutionary PDEs. Journal of Geometry and Physics 57 (2006), 101-119. (with S.-Q. Liu)

20. Bihamiltonian systems of hydrodynamic type and reciprocal transformations. Letters in Mathematical Physics 75 (2006), 79-92. (with T. Xue)

21. Deformations of semisimple bihamiltonian structures of hydrodynamic type. Journal of Geometry and Physics 54 (2005), 427-453. (with S.-Q. Liu)

22. Virasoro symmetries of the extended Toda hierarchy. Communications in Mathematical Physics 250 (2004), 161-193. (with B. Dubrovin)

23. The extended Toda hierarchy. Moscow Mathematical Journal 4 (2004), 313-332. (with G. Carlet, B. Dubrovin)

24. Deformations of the bihamiltonian structures on the loop space of Frobenius manifolds. Journal of Nonlinear Mathematical Physics 9 (2002), Suppl. 1, 243-257.

25. On the CP^1 topological sigma model and the Toda lattice hierarchy. Journal of Geometry and Physics 40 (2002), 215-232.

26. Frobenius manifolds and Virasoro constraints. Selecta Mathematica, New Series 5 (1999), 423-466. (with B. Dubrovin)

27. Bihamiltonian hierarchies in 2D topological field theory at one-loop approximation. Communications in Mathematical Physics 198 (1998), 311-361. (with B. Dubrovin)

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

29. On Segal-Wilson's construction for the tau-functions of the constrained KP hierarchies. Letters in Mathematical Physics 36 (1996), 1-15.

30. A remark on the representation theory of the algebra U_q(sl(n)) when q is a root of unity. Journal of Physics A: Math. Gen. 25 (1991), 851-859.

人才培养

三名硕士毕业生目前分别任墨尔本大学数学与统计系讲师、丘成桐数学科学中心助理教授、南开大学陈省身数学研究所特聘研究员;七位博士毕业生中三位分别任清华大学数学科学系教授(于2017年获国家杰出青年基金)、中国科学技术大学数学科学学院教授(于2018年入选国家青年千人计划)、中山大学数学学院副教授。