U.S.-Germany Dissertation Enhancement: Serre Duality for Systems of Submodules

美德论文增强：子模块系统的 Serre 对偶性

• 批准号: 0831369
• 负责人: Markus Schmidmeier
• 金额: $ 0.93万
• 依托单位: Florida Atlantic University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-10-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0831369&HistoricalAwards=false
• 关键词: U.S.; Germany; Dissertation; Enhancement; Serre

U.S-Germany Dissertation Enhancement: Serre Duality for Systems of Submodules0831369The purpose of this Doctoral Dissertation Enhancement Project is to further the research in mathematics conducted by Audrey Doughty, doctoral student at Florida Atlantic University, on her thesis topic in the representation theory of finite dimensional algebras. Ms. Doughty's dissertation advisor is Associate Professor Markus Schmidmeier. The award will allow Ms. Doughty to visit the Collaborative Research Center 701 at Bielefeld University in Germany and work with Professor Claus M. Ringel on the following topics: use of homological methods, in particular Serre duality, for the classification of systems of submodule embeddings; applications to the problem posed in 1934 by Garrett Birkhoff of the classification of the possible subgroups of finite abelian groups, and to the Invariant Subspace Problem in operator theory; and computation of the precise values of the Calabi-Yau dimension of submodule embedding categories in important examples. The project will expand on an existing collaboration between researchers at Florida Atlantic University and at Bielefeld University. Its success will improve opportunities for research and graduate studies in mathematics in Southeastern Florida.

美德论文增强：子模块系统的塞尔对偶性0831369该博士论文增强项目的目的是进一步推进佛罗里达大西洋大学博士生 Audrey Doughty 的数学研究，其论文主题为有限维代数表示论。 Doughty 女士的论文导师是 Markus Schmidmeier 副教授。 该奖项将使 Doughty 女士能够访问德国比勒菲尔德大学的合作研究中心 701，并与 Claus M. Ringel 教授就以下主题进行合作：使用同源方法，特别是 Serre 对偶性，对子模块嵌入系统进行分类；应用于 Garrett Birkhoff 于 1934 年提出的有限阿贝尔群的可能子群分类问题，以及算子理论中的不变子空间问题；以及计算重要示例中子模块嵌入类别的 Calabi-Yau 维数的精确值。 该项目将扩大佛罗里达大西洋大学和比勒菲尔德大学研究人员之间现有的合作。 它的成功将增加佛罗里达州东南部数学研究和研究生学习的机会。