朱 彬

湖南 汉寿人

博士(1999,比勒费尔德);教授,博导

 

 

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

2013.9-2014.2, 高等代数,数学系2013级.教材:高等代数学,姚慕生,吴泉水编,复旦大学出版社

2013.2-2013.7,同调代数与交换代数,研究生课

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.

     

Visitors:

2017

S.Koenig(Stuttgart),K.Yamagata(Tokyo)

A.Buan(NTNU, Trondheim);K.Igusa(Brandeis Univ.) Shiping Liu(Univ. Sherbrooke); G.Todorov(Northeastern Univ.)

Yu Zhou(NTNU, Trondheim), Yu Liu(Uppsala Univ.)

2016

Hiroyuki Nakaoka (Kagishima), 1.11.2016--4.11.2016

Shiping Liu(Sherbrooke),

Yu Zhou(NTNU)

2015

 

 

近期会议

2017年

10 - 13. July. International Workshop on Cluster Algebras and Related Topics. Chern Institute of Mathematics, Nankai University,

Tianjin, China.

 

2016年

19 - 23. Dec. Master Lectures--the Legacy of Emmy Noether and Gottingen mathematics. Tsinghua Sanya International Mathematics Forum in Sanya, Hainan Province

28 - 31. Oct. 第四届环与代数workshop.江苏理工学院(江苏省常州市)

10-19. Aug. Workshop and International Conference on Representations of Algebras (ICRA 2016),Syracuse, USA.

 

2015年

20 -25. Jun, 第十七届全国代数表示论会议. 山东大学数学科学学院

20-22, March. Workshop on non-commutative algebras and geometry, Zhejiang Normal University, Jinhua, China

 

2014年

Workshop and International Conference on Representation Theory of Algebras (ICRA 2014), China

 

2013年

29 July-03.Aug, 第十五届全国代数表示论会议. 四川大学数学科学学院

24-28,June, Triangulated Categories in Representation Theory of Algebras, PRIMA 2013, Shanghai Jiaotong University.

10-16,June, The Third International Symposium on Groups, Algebras and related topics in Beijing, celebrating the 50th

anniversary of the Journal of Algebra . Peking University

 

2012年

12月1-5,第二届海峡两岸代数研讨会,台湾成功大学

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.

 

Papers

 

Recent Preprints

 

2017:

 

 

47. Cotorsion pairs in cluster categories of type A_{\infty}^{\infty}(with Huimin Chang and Yu Zhou), see arXiv.1704.04019

 

46. Singularity categories of Gorenstein monomial algebras (with Ming Lu), see arXiv:1708.00311

 

2016:

 

45. Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories (with Wen Chang and Panyue Zhou), see arXiv:1610.05006

 

44. Torsion pairs in finite 2-Calabi-Yau triangulated categories with maximal rigid objects (with Huimin Chang), see arXiv:1608.03734

 

43.Triangulated quotient categories revisited (with Panyue Zhou), see arXiv:1608.000297

 

2015:

 

42.Cluster automorphism groups and automorphism groups of exchange graphs (with Wen Chang), see arXiv:1506.02029

 

41.Cluster automorphism groups of cluster algebras of finite type (with Wen Chang). J. Algebra 447, 49-515, 2016. see arXiv:1506.01950

 

40. Ghost tilting objects in triangulated categories (with Wuzhong Yang),see arXiv:1506.00093;

Title is changed as "Relative cluster tilting

objects in triangulated categories". To appear in Trans AMS.

 

39. On the automorphism groups of cluster algebras with coefficients (with Wen Chang), Sciences in China (Mathematics), Vol.59(10),

1919-1936, 2016.arXiv:1506.01942

 

2014:

 

38. On rooted cluster morphisms and cluster structures in 2-Calabi-Yau triangulated categories (with Wen Chang),

J. Algebra 458, 387-421, 2016. See arXiv:1410.5702 .

 

37. On cluster-tilting objects in triangulated categories with Serre duality (with Wuzhong Yang and Jie Zhang),

pdfComm Alg 45(1),299-311,2017.

 

 

36. On support tau-tilting modules over endomorphism algebras of rigid objects(with Wen Chang and Jie Zhang),

Acta Sinica Math (New Series), &Vol.31(9), 1508-1516(2015).

 

2011:

 

35. Mutation of torsion pairs in triangulated categories and its geometric realization (with Yu Zhou), pdf. See arXiv:1105.3521 .

 

Published Papers(1999-):

34. T-structures and torsion pairs in a 2-Calabi-Yau triangulated category (with Yu Zhou), pdf(2012-12-28), pdf(2013-07-18), Jour. Lond.Math.Soc.89(1),213-234,2014.

33. Cotorsion pairs in the cluster category of a marked surface (with Jie Zhang, Yu Zhou), pdf (2012-04-29).pdf(2013-07-05), J. Algebra.391,209-226,2013.

 

32. Triangulated quotient categories (With Yu Liu), pdf, pdf(2013-06), Comm. Alg.41(10),3720-3738,2013.. See also arXiv:1024.2024 .

 

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. Jour. Lond.Math.Soc 89(3),703-723, 2014.

 

30. Finite repetitive generalized cluster complexes and d-cluster categories (with Teng Zou), pdf. Algebra Colloquium, 20 (1), 123-140,2013.

 

29. Maximal rigid subcategories in 2-Calabi-Yau triangulated categories (with Yu Zhou), pdf(2011-9) . Journal of Algebra 348, 49-60, 2011. See also arXiv:1004.5475.

 

28.Cluster-tilted algebras and their intermediate coverings, pdf . Communications in Algebra, 39,2437-2448.2011. See also arXiv:0808.2352.

 

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

 

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

 

25. 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.

 

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

 

23. Preprojective cluster variables of acyclic cluster algebras, dvi. Comm Algebra. 35. 2857-2871, 2007. see also arXiv:     math.RT/0511706.

 

22. Applications of BGP-reflection functors: isomorphisms of cluster algebras, dvi Sciences in China (Mathematics), Vol.49(12), 1839-1854, 2006.  

 

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.

 

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.

 

19. Separable bimodules and approximations (with S. Caenepeel ), ps, 2002. Algebras and Representation Theory, Vol.8, 207-223, 2005.

 

18. Locally finite triangulated categories (with J.Xiao), pdf, 2003. Journal of Algebra, 290, 473-490,2005.

 

17. BGP-reflection functors in root categories (with J.Xiao and Guanglian Zhang),dvi. Sciences in China (Mathematics), Vol.48(8), 1033-1045, 2005.

 

16. On characteristic modules of quasi-hereditary graded algebras, dvi, Communications in Algebra. Vol. 32, 2919- 2928, 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.

 

14.On Delta-good filtration dimensions of standardly stratified algebras (with S. Caenepeel ) pdf. Communications in Algebra. Vol.32, 1603-1614, 2004.

 

13. The structure of gr-simple rings, ps, dvi. Northeast Math. J. Vol.19(3), 231-234. (2003).

 

12.Relative Approximations and Maschke Functors, pdf. Bulletin of Australian Mathematical society, Vol.67, 219-224(2003).

 

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).

 

10.Relations for Grothendieck Groups of Triangulated categories (with Jie Xiao), pdf. Journal of Algebra, Vol.257, 37-50(2002).

 

9.On Delta-good module categories arising from hereditary algebras. Communications in Algebra, Vol.29(12), 5575-5588(2001).

 

8.Contravariantly finite subcategories and adjunctions, dvi. Algebra Colloquium, Vol.8(3),307-314(2001).

 

7.Contravariantly finite subcategories in a tilting torsion class. Progress in Nature Sciences, Vol.11(10),797-800 (2001).

 

6.Triangular matrix algebras over quasi-hereditary algebras. Tsukuba Journal of Mathematics, Vol.25(1),1-11(2001).

 

5. A criterion for coils, pdf,. Communications in Algebra, Vol.29(1), 253-269(2001).

 

4.Coils for vectorspace categories, pdf,. Communications in Algebra, Vol.29(3), 1191-1214 (2001).

 

3.On Delta-good module categories without short cycles (with Bangming Deng). Proc. Amer. Math. Soc., Vol.129(1), 69-77(2001).

 

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).

 

1.Smash Products of Quasi-hereditary Graded Algebras, pdf. Archive der Mathematik, Vol.72(6), 433-437 (1999)

 

Links

    Algebras and Representations at Tsinghua