朱 彬

湖南 汉寿人

博士(1999，比勒费尔德)；教授,博导

基础数学所所长

 

北京清华大学数学科学系,

邮编：100084

办公室： 理学院楼 (数学系) 1208房间

Tel: +86(0)10-62772862

Fax: +86(0)10-62785847

Email: bzhu@math.tsinghua.edu.cn

    English version

 

教学

2011.9-2012.2, 高等代数,数学系2011级.教材:高等代数学,姚慕生,吴泉水编,复旦大学出版社

2011.2-2011.6,代数与几何(2),

2010.9-2011.1, 抽象代数(1). 基科9字班，数学双学位

教材： 姚慕生编著， 抽象代数学， 复旦出版社.

2010.3-2010.7, 几何与代数（1），建筑学院09级.

2009.9-2010.1. 抽象代数（II），研究生课.

2009.2-2009.7, 几何与代数(2).

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.

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.

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

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


 

简历

  • 学习经历:
    • 1997.10-1999.3, 德国比勒费尔德大学数学学院博士研究生. 导师: C.M.Ringel教授.
    • 1995.9-1997.9, 北京师范大学数学系博士研究生. 导师: 刘绍学教授.
    • 1986.9-1989.7, 吉林师范大学数学系硕士研究生.
    • 1982.9-1986.7, 湖南师范大学数学系本科生.
  • 工作，访问经历:
    • 2005.9-2006.9, 访问德国 帕德博恩大学， 科隆大学， 比勒费尔德大学.
    • 2004.7-2004.9, 访问英国莱士特大学.
    • 2002.2-2002.5, 访问比利时布鲁塞尔大学(VUB).
    • 2001.5 - , 清华大学数学科学系教师: 讲师，副教授，教授，博士生导师
    • 1999.6-2001.4, 清华大学数学科学系博士后.

     

     

近期会议

 

 

2012年

8月8-17, Workshop and International Conference on Representations of Algebras (ICRA 2012)
University of Bielefeld, Germany

6月22-27， 第十四届全国代数表示论会议. 安徽大学数学 科学学院与中国科学技术大学数学科学学院主办

3月28-30，Cluster categories and cluster tilting, A conference honoring Idun Reiten on the occasion of her 70th birthday
NTNU, Trondheim, Norway.

 

2011年

10月2-7， 上海国际代数表示论会议, 上海交大数学系.

9月26-30，Workshop on representation theory: Cohomology and support. 晨兴数学中心,中科院数学与系统科学研究院(参与主办)

9月4-9, Workshop:Cluster algebras, representation theory, and Poisson geomery. BIRS, Banff, Canada.

7月10-15，海峡两岸代数研讨会，厦门大学

6月12-15，Workshop on Algebras and Representation Theory，山东大学数学学院.

 

 

2008年

10月19-25, 第十一届全国代数会(张家界),湘谭大学主办. 做大会邀请报告: Some related studies on cluster algebras

8 月25-29, 第十届中国代数表示论workshop（南京大学）.

2月17-23, Representation Theory of Finite Dimensional Algebras, Mathemtisches Forschungsinstitut Oberwolfach， Germany. 做邀请报告:d-cluster tiltings in d-cluster categories and their combinatorics

 

2007年

9月10-14, 参与主办 Workshop on Categorification, Quantization and Clusters, Morningside Center of Mathematics, Chinese Academy of Sciences.

8月27-9月1, 中国第九届代数表示论Workshop (北京工业大学) 做邀请报告: Cluster tilting theory .

8月20-25, ICRA XII (Torun, Poland) 做报告:d-Cluster tiltings in d-cluster categories.

8月18-20, 参与主办"International conference on algebras --万哲先院士生日庆祝会" (清华大学).

 

2006年

10月3-8, 中国第八届代数表示论Workshop (浙江大学) 做邀请报告: Cluster categories and cluster algebras.

9月18-22, Workshop on non-commutative algebraic Geometry(Fudan Univ.) 做邀请报告: From triangulated categories to abelian categories.

7月7-9, Perspectives in Representation Theory, Physikzentrum Bad Honnef(Germany).

5月23-25, Workshop on cluster algebras and cluster-tilted algebras, University of Bielefeld, Germany. 做邀请报告: A generalization of cluster tilted algebras.

 

2005年

8月22-26, 参与主办International summer school on derived categories in representation theory and 7th national workshop on representation theory of algebras at Tsinghua University.

5月29-30, Workshop on Homology, Geometry, and Combinatorics of Representations in the Sino-German Science Center in Beijing 做邀请报告: BGP-reflection functors in cluster categories and applications

5月23-28,International AsiaLink conference on algebras and representations at Beijing Normal University.

3月20-24, Workshop on D-branes and duality on Strings, USTC Shanghai institute for advanced studies. 做邀请报告: Locally finite triangulated categories.

2004年

7月7-16, Workshop on noncommutative algebras, University of Warwick, UK. 作报告: Locally finite triangulated categories.

 

2003年

8月3-4,中国第六届代数表示论Workshop (厦门大学), 做邀请报告: On triangulated categories of finite type.

7月29-8月2, 中国第八届李代数会议(厦门大学), 做邀请报告: On good filtration dimension and finitistic dimension for stratified algebras.

 

研究兴趣，领域

  • Cluster tilting theory, cluster categories and Calabi-Yau categories
  • Cluster algebras and Calabi-Yau algebras
  • Derived categories and triangulated categories.
  • Quasi-hereditary algebras and relatives.
  • Auslander-Reiten Theory.

 

发表论文

  • 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.

 

已完成论文

27. Cluster combinatorics of d-cluster categories (with Yu Zhou ), dvi. Journal of Algebra, 321, 2898-2915,2009. See also arXiv: arXiv:0712.1381.

28. Cluster-tilted algebras and their intermediate coverings, pdf. Comm Alg.39, 2437-2448, 2011. See also arXiv: arXiv:0808.2352.

29.Finite repetitive generalized cluster complexes and d-cluster categories (with Teng Zou), Algebra Colloquium(to appear).

30. Maximal rigid subcategories in 2-Calabi-Yau triangulated categories (with Yu Zhou) pdf. , version 2(2011-09), Journal of Algebra 348, 49-60, 2011. See also arXiv: 1004.5475.

31. Cluster algebras of type C via cluster tubes (with Yu Zhou), pdf. Title changed as "Cluster algebras arising from cluster tubes". See also arXiv:1008.3444.

32. Mutation of torsion pairs in triangulated categories and its geometric realization (with Yu Zhou) pdf .

33. Triangulated quotient categories (with Yu Liu), pdf, Comm. Alg.

34. Cotorsion pairs in the cluster category of a marked surface (with Jie Zhang, Yu Zhou), pdf(2012-04-29)

 

Links

    Algebras and Representations at Tsinghua