BIN ZHU (朱彬)

Professor

Department of Mathematical Sciences,

Tsinghua University,

Beijing 100084, P.R.China

Tel: +86(0)1062772023

Fax: +86(0)1062785847

Email: bzhu@math.tsinghua.edu.cn

 

Teaching (教学）

  • 2006 9---2007 1, 线性代数（1）， 经管学院（61-64班）， 教材：线性代数，李炯生，查建国编著，中国科技大学出版社 ;
  • 2007 2---2007 7, 线性代数（2），经管学院（61-64班）， 教材：线性代数，李炯生，查建国编著，中国科技大学出版社
    参考书：1。高等代数学，张贤科等编著，清华大学出版社; 2。高等代数，张禾瑞等编，高等教育出版社； 3. 理工科代数基础， 俞正光等编清华清华大学出版社。
    讲义： Jordan标准形 ； 欧氏空间 :
  • 2007 9---2008 1,
    线性代数（1）， 经管学院71-75；教材：线性代数与解析几何，俞正光，李永乐，詹汉生编，清华大学出版社
    几何与代数（1）, 环71-73， 材料71-73， 教材：线性代数与解析几何，俞正光，李永乐，詹汉生编，清华大学出版社
  • 2008 2---2008 7, Topics in Representation Theory: Derived categories and tilting theory; (with Jie Xiao).
    参考书：
    1． Amnon Neeman, Triangulated categories, Annals of Mathematics Studies 148, 2001, Princeton Univ. Press.
    2. M. Kashiwara, P. Schapira, Sheaves on Manifolds 1990, Springer.
    3．D.Happel, Triangulated categories in representation theory of algebras, Lecture Note Series 119, London Math. Soc.1988.
  • 2008 9---2009 1,
    几何与代数（1）, 分8，化81-83，化学81-82，基科89， 教材：线性代数与几何（上），俞正光等编，清华大学出版社

Brief CV

  • Education:
    • Oct.1997-Mar.1999, Ph.D. student in Falkultaet fuer Mathematik at Universitaet Bielefeld.
      Supervisor: Professor Dr. C.M.Ringel.
    • Sept.1995-Sept.1997, Ph.D. student in Department of Mathematics at Beijing Normal University.
      Supervisor: Professor Shaoxue Liu.
    • Sept.1986-Jul.1989, Graduate student at Department of Mathematics at Jilin Normal University.
    • Sept.1982-Jul.1986, Undergraduate student at Department of Mathematics at Hunan Normal University.
  • Professional background:
  • Conferences:
    • July. 29-Aug. 2, 2003, 8th National conference on Lie algebras, University of Xiamen, Xiamen, China;
      invited talk: On good filtration dimension and finitistic dimension for stratified algebras.
    • Sept.24-Sept.27,2002, Advanced Seminar on Representation theory of Heck algebras and cellular algebras", Beijing Normal University, Beijing, China;
      invited talk: On good filtration dimensions for quasi-hereditary algebras.
    • Aug.29-Sep.3,2002, International Conference on Algebra--A Satellite Conference of ICM2002, Suzhou University, China;
      invited talk: Relations of Grothendieck groups of triangulated categories.
    • April. 16. 2002, Workshop at Antwerpen: Hopf algebras, noncommutative geometry and separable bimodules, Antwerpen, Belgium;
      invited talk: Separable bimodules and approximations.
    • Aug. 21-Sep.1,2000, The Ninth International Conference on the Representation Theory of Algebras, Beijing, China;
      invited talk: On Delta-good module categories arising from hereditary algebras.
    • Oct.10-14, 1999, 7th national comference on algebras, Beijing Normal University;
      invited talk: Relations for Grothendieck Groups of Quasi-Hereditary Algebras.
    • Aug. 31-Sep.4,1998, The 8.5th International Conference on the Representation Theory of Algebras, Bielefeld, Germany;
      the title of talk: Some combinatorial descriptions of coils.
    • Sep.7-Sep.11,1998, Workshop on Infinite dimensional modules, Bielefeld, Germany.

 

Research Interests

  • Representation Theory of Artin Algberas: Auslander-Reiten components of Artin Algberas; Vectorspace Categories; Quasi-hereditary Algebras and related algebras.
  • Homologiacl Algebras: Homological Dimensions; Exact Categories; Derived Categories and Triangulated Categories.

 

Papers and Preprints

  • Publications(1999-)
    1. Smash Products of Quasi-hereditary Graded Algebras, pdf. Archive der Mathematik, Vol.72(6), 433-437 (1999).
    2. Relations for Grothendieck Groups of Quasi-hereditary algebras. Chinese Journal of Contemporary Mathematics Vol.22(2), 119-124(2001), A Chinese version appeared in Chin. Ann. of Math (A), Vol.22(2), 135-140(2001).
    3. On Delta-good module categories without short cycles (with Bangming Deng). Proc. Amer. Math. Soc., Vol.129(1), 69-77(2001).
    4. Coils for vectorspace categories, pdf,. Communications in Algebra, Vol.29(3), 1191-1214 (2001).
    5. A criterion for coils, pdf,. Communications in Algebra, Vol.29(1), 253-269(2001).
    6. Triangular matrix algebras over quasi-hereditary algebras. Tsukuba Journal of Mathematics, Vol.25(1),1-11(2001).
    7. Contravariantly finite subcategories in a tilting torsion class. Progress in Nature Sciences, Vol.11(10),797-800 (2001).
    8. Contravariantly finite subcategories and adjunctions, dvi. Algebra Colloquium, Vol.8(3),307-314(2001).
    9. On Delta-good module categories arising from hereditary algebras. Communications in Algebra, Vol.29(12), 5575-5588(2001).
    10. Relations for Grothendieck Groups of Triangulated categories (with Jie Xiao), pdf. Journal of Algebra, Vol.257, 37-50(2002).
    11. A condition for a translation quiver to be a coil (with Zongyi Hu). Acta Sinica Math (New Series), Vol.19(1), 107-126(2003).
    12. Relative Approximations and Maschke Functors, pdf. Bulletin of Australian Mathematical society, Vol.67, 219-224(2003).
    13. The structure of gr-simple rings, ps, dvi. Northeast Math. J. Vol.19(3), 231-234. (2003).
    14. On Delta-good filtration dimensions of standardly stratified algebras (with S. Caenepeel) pdf. Communications in Algebra. Vol.32, 1603-1614, 2004.
    15. Finitistic dimension and good filtration dimensions of stratified algebras (with S.G.Wang). Bulletin of Australian Mathematical society, Vol.69, 341-347, 2004.
    16. On characteristic modules of quasi-hereditary graded algebras, dvi, Communications in Algebra. Vol. 32, 2919- 2928, 2004.
    17. BGP-reflection functors in root categories (with J.Xiao and Guanglian Zhang),dvi. Sciences in China (Mathematics), Vol.48(8), 1033-1045, 2005.
    18. Locally finite triangulated categories (with J.Xiao), pdf, 2003. Journal of Algebra, 290, 473-490,2005.
    19. Separable bimodules and approximations (with S. Caenepeel), ps, 2002. Algebras and Representation Theory, Vol.8, 207-223, 2005.
    20. BGP-reflection functors and cluster combinatorics, pdf, 2004. Journal of pure and applied algebra, Vol.209, 497-506, 2007. See also arXiv: math.RT/0511380.
    21. Tilting theory in cluster categories of hereditary abelian categories, dvi. Appeared in Journal of Algebra, Vol.304, 832-850,2006 with a new title "Equivalences between cluster categories“. See also arXiv: math.RT/0511382.
    22. Applications of BGP-reflection functors: isomorphisms of cluster algebras, dvi Sciences in China (Mathematics), Vol.49(12), 1839-1854, 2006.  
    23. Preprojective cluster variables of acyclic cluster algebras, dvi. Comm Algebra. 35. 2857-2871, 2007. see also arXiv:     math.RT/0511706.

    24. From triangulated categories to abelian categories \\ -- cluster tilting in a general framework} (with S. Koenig), dvi, appeared in Math.Zeit. 258(1), 143-160, 2008.. See also arXiv: math.RT/0605100.

    25. Generalized Cluster Complexes via Quiver Representations, dvi, 2006. Appeared in Journal of Algebraic Combinatorics 27, 25-54, 2008. See also arXiv: math.RT/0607155.

    26. d-Cluster tiltings in d-cluster categories and their combinatorics (with Yu Zhou), Oberwolfach Report Vol. 5(1), 453-454, 2008.

 

  • Preprints

27.Cluster combinatorics of d-cluster categories (with Yu Zhou), dvi. See also arXiv: arXiv:0712.1381.

28.Cluster-tilted algebras and their intermediate coverings, pdf. See also arXiv: arXiv:0808.2352.

 

Links

    Algebras and Representations at Tsinghua