时间：2023年12月28日
地点：后主楼1220
目的: 介绍代数和表示论中出现的各种簇以及这些簇在代数和表示论中的应用。
时间：8:30-9:30
题目：Algebras and varieties
报告人：邢博涵
摘要：In this talk, I will introduce the work of E.L.Green, L.Hille and S.Schroll in which they construct a class of new affine algebraic varieties whose points correspond to quiver algebras by using the theory of Gröbner bases. We can also see that the algebras in this variety have many common properties.
时间：9:45-10:45
题目：The varieties of modules and Poisson structures
报告人：文灿
摘要：In this talk, we firstly explain the schemes from the point of functors, then recall the variety/scheme of modules and give some examples. As an application, we show that a Poisson structure can be induced on the affine moduli space of (semisimple) representations of an associative algebra from a suitable Lie algebra structure on the zeroth Hochschild homology of the algebra. This is a retelling of the results of William Crawley-Boevey.
时间：12:30-13:30
题目：Parabolic and Borel subgroups of linear algebraic groups
报告人：黄飞越
摘要：This talk is an overview of the theory of parabolic and Borel subgroups, based on Springer's monograph on linear algebraic groups. We will introduce basic properties of these subgroups via the concept of complete varieties. The conjugacy theorems for Borel groups and maximal tori will then be treated. As an important result, we will give the structure theory of connected solvable groups.
时间：13:45-14:45
题目：The number of isomorphism classes of tilting complexes of given dimension is finite
报告人：李能群
摘要：In “Geometry of chain complexes and outer automorphisms under derived equivalence”, Huisgen-Zimmermann and Saorín show the following result: Let A be a finite dimensional algebra over an algebraically closed field, then for any finite sequence of non-negative integers, there are only finitely many complexes X of projective A-modules with this sequence of dimensions such that Hom_{D^b(A)} (X, X[1]) = 0. We will give a brief introduction to the proof of this theorem.
组织者：刘玉明
