# Fan Xu

Department of Mathematical Sciences
Tsinghua University
Beijing, 100084, P. R. China

E-mail: fanxu at math.tsinghua.edu.cn

## Teaching

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## Publications

[10]  (With Xueqing Chen) A geomertization of the Happel functor, to appear in Mathematical Reports of the Academy of Science of the Royal Society of Canada.

[9]  (With Jie Sheng) Derived Hall algebras and lattice algebras, to appear in Algebra Colloquium.

[8]  (With Ming Ding) A \$\mathbb{Z}\$-basis for the cluster algebra of type \$\widetilde{D}_4\$, to appear in Algebra Colloquium.

[7]  (With Jie Xiao) Green's formula with \$\mathbb{C}^{*}\$-action and Caldero-Keller's formula for cluster algebras, to appear in Prog. Math, Birh\"auser.

[6]  (With Ming Ding and Jie Xiao) Realizing Enveloping Algebras via Varieties of Modules, to appear in Acta Math. Sinica.

[5]  On the cluster multiplication theorem for acyclic cluster algebras, Transaction A.M.S., 362 (2010), no.2, 753- 776.

[4]  (With Jie Xiao) A multiplication formula for module subcategories of Ext-symmetry, Proceedings A.M.S., 137 (2009), no.8, 2517-2528.

[3]  (With Jie Xiao) Green formula in Hall algebras and cluster algebras, µÚËÄ½ì¹ú¼Ê»ªÈËÊýÑ§¼Ò´ó»á 2007, Vol I, 252-285.

[2]  (With Jie Xiao) Hall algebras associated to triangulated categories, Duke Math. J. Vol. 143 (2008), no.2, 357-373.

[1]  A note on the fundamental group of a triangular algebra, Algebra Colloq. Vol. 15 (2008), no.3, 371-378 .

## Preprints

[1]  (With Jie Xiao and Guanglian Zhang) Derived categories and Lie algebras, arXiv: 0604564.

[2]  Hall algebras associated to triangulated categories, II: almost associativity, arXiv: 0710. 5588.

[3]  (With Ming Ding and Jie Xiao) Integral bases of cluster algebras and representations of tame quivers, arXiv: 0901.1937.

[4]  (With Xueqing Chen) Hall algebras for odd periodic triangulated categories , arXiv:1001.4353.

[5]  (With Ming Ding ) The cluster character for cyclic quivers, arXiv:1001.4360.

[6]  (With Ming Ding ) Notes on the cluster multiplication formulas for 2-Calabi-Yau categories, arXiv: 1001.4365.

[7]  (With Ming Ding) Bases of the quantum cluster algebra of the Kronecker quiver, arXiv:1004.2349.

## Talks

[1]  Talk at Workshop on representations and categorifications, April 15-16, 2010. Talk's slides.

[2]  Talk at Conference on Interplay between Representation Theory and Geometry, May 3-7, 2010. Talk's slides.