讲座题目1：Introduction to Nakajima quiver varieties

讲座时间：2019-07-11 9:30-11:30

讲座内容：We will address basic concepts of geometric invariant theory and review the definition of Nakajima quiver varieties. We will also address their relation to representation theory of Kac-Moody Lie algebras.

讲座题目2：Hall Algebras and Quantum Cluster Algebras (I)

讲座时间：2019-07-12 9:30-11:30

讲座内容：Through the Ringel-Hall algebra approach, one can construct quantum groups from some abelian categories, and construct Kac-Moody Lie algebras and some elliptic Lie algebras from the derived categories of some finite dimensional associative algebras. In this talk, the constructions of Hall algebras of some triangulated categories via derived Hall algebras for derived categories will be presented and the relations between them will be characterized.

讲座题目3：Hall Algebras and Quantum Cluster Algebras (II)

讲座时间：2019-07-12 14:30-16:30

讲座内容：We will address some connections between Hall algebras and quantum cluster algebra.

讲座题目4：Generalized quantum cluster algebras and Laurent phenomenon

讲座时间：2019-07-13 9:30-11:30

讲座内容：We define a quantum analogue of a class of generalized cluster algebras, which can be viewed as a generalization of quantum cluster algebras defined by Berenstein and Zelevinsky. We also prove the Laurent phenomenon of these generalized quantum cluster algebras.  This talk is based on joint works with L. Bai, M. Ding and F. Xu.

讲座题目5：Hall algebras and perverse sheaf algebras

讲座时间：2019-07-13 14:30-16:30

讲座内容：In this survey talk, we will discuss Lusztig’s work on an algebra of perverse sheaves and will address its relations with Ringel-Hall algebras and quantum groups. The connections between representations of quivers and perverse sheaves will be briefly described.

讲座人简介：

陈学庆，男，美国University of Wisconsin–Whitewater教授。1989-1993年就读于bv伟德国际体育数学与信息科学学院，论文导师为李会师教授；1993-1996年就读于北京师范大学，师从肖杰教授；1997-2002年就读于加拿大Carleton University，师从Dlab教授。2002-2004年在University of Ottawa任NSERC Postdoctoral Fellow，2005年至今任职于美国University of Wisconsin–Whitewater。
其研究兴趣集中在Representation Theory of Finite Dimensional Algebras 、Hall Algebras and Related Topics in Quantum Groups and Kac–Moody Lie Algebras、Derived Categories and Triangulated Categories、Cluster Algebras and Cluster Categories、Stratified Algebras and Category O、Nonassociative Algebras and Their Automorphism Groups等方面，特别是在Hall Algebra方面，其早期关于Hall Algebra的硕士论文Exceptional Sequence in Hall Algebra and Quantum Group见诸Compositio Math.