讲座人简介：

林宗柱，美国堪萨斯州立大学终身教授，博士生导师，主要从事表示论、代数群以及量子群等方面的研究，在 Invent. Math.，Adv. Math., Trans. Amer. Math. Soc., CMP 和J. Algebra 等重要学术期刊上发表论文数十篇，标志性成果包括林-Nakano定理，出版学术著作五部。

讲座简介：

In the process of contructing quantun enveloping algebras from a geometric approach,

Lusztig discovered a natural basis for the positive half of the quantum enveloping algebra of kac-Moody Lie algebra, in terms of simple perverse sheaves.

This basis has remarkable properties. The geometric construction of the quantum enveloping algebra involving the geometric construction of hall multiplications of Serre generators. The products of this Serre generators constitutes only a small part of the geometric Hall algebra. These products are exactly the monomials of Serre generators. The construction of these monomials is a quiver version of semisimple complexes of sheaves supported over nilpotent varieties coming from Springer resolutions of the Lie algebra of a reductive group. In this talk I will summarize the relations among different bases: PBW basis, monomial basis, and canonical basis. How are they related to Springer resolutions of reductive groups and what these bases mean in the case of reductive groups, and how these constructions can be generalized.