报告人：Henning Krause教授，德国Bielefeld大学

题目: Linear representations of posets - from concrete to abstract

时间: 3月19日10:00-11:00, 教室: 2404

Abstract: For any finite totally ordered set and any field, the finite dimensional linear representations form an abelian category. Various classes of subcategories admit natural combinatorial descriptions, and counting them yields familiar integer sequences. Surprisingly, in some cases new integer sequences arise. These examples will be discussed in the first part of my talk. The formulation of such counting problems leads to the construction of a universal category of poset representations which does not depend on the choice of any ring of coefficients. The second part of the talk is devoted to a more abstract perspective, providing a characterisation of those length categories that arise as categories of linear poset representations.

题目：Serre's theorem for coherent sheaves via Auslander's techniques

时间：3月20日, 14:00-15:00, 教室: 2403

Abstract: Serre's theorem relating coherent sheaves on a projective variety to graded modules over some appropriate graded ring is a cornerstone of non-commutative geometry, for instance by the non-commutative analogue of this theorem due to Artin and Zhang. My talk will present a new version of this theorem which does not require any noetherianess assumptions. The proof uses Auslander's theory of coherent functors. A theorem of Lenzing for representations of hereditary algebras is given as an application.

报告人简介：Henning Krause，德国Bielefeld大学W3教授，著名代数学家，曾任德国Paderbom大学C4教授和中国科学技术大学客座教授，任著名期刊Adv. Math. 编委，是挪威皇家科学与文学院院士和美国数学会会士，在代数的稳定等价、三角范畴的局部化理论以及三角范畴的支撑簇理论等方面做出重要贡献。