活动地点：

活动类型：学术报告

主讲人：Prof. Andrey Todorov and Prof. Zongzhu Lin

活动时间：

活动内容：

1．Lecturer: Prof. Andrey Todorov
(Dept. of Math., UC Santa Cruz)
Title: Generalized Kummer Varieties and Locally Symmetric spaces 

Abstract:
In this talk I will review  the classical Kummer surfaces. These are quartic hypersurfaces in the projective three dimensional complex manifold with 16 singular points. Then I will review some elementary facts about Riemann surfaces. I will describe how one can generalize to higher dimension the Kummer construction to higher dimension and obtain interesting Calabi-Yau manifolds, whose moduli space is a locally symmetric space. It is very rare that locally symmetric space is a moduli space of CY manifolds. This the first non-trivial example.

2 Lecturer: Prof. Zongzhu Lin
(Dept. of Math., Kansas State Univ.)
Title: Canonical Bases for affine quantum groups

Abstract:
In this talk we will discuss various constructions of bases for quantum groups by algebraic, geometric, and representation theory approaches. In the finite type cases, due to the fact that root spaces of Lie algebras are 1-dimensional and the Weyl group has a longest element, it is not difficulty to understand the relations among different constructions in terms of PBW type bases. In affine cases, PBW-type bases does not make sense and  some of the construction does not work. We will give different approaches to the descriptions of canonical basis.