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.

美国-德国论文增强：Serre对偶系统的Submodules 0831369这个博士论文增强项目的目的是进一步的研究在数学进行的奥黛丽多尔蒂，博士生在佛罗里达大西洋大学，她的论文题目在表示理论的有限维代数。 Doughty女士的论文导师是副教授Markus Schmidmeier。 该奖项将允许多尔蒂女士访问德国比勒费尔德大学的701合作研究中心，并与克劳斯M。林格尔对以下议题：使用同调的方法，特别是塞尔对偶，分类系统的子模块嵌入;应用程序的问题提出了在1934年由加勒特伯克霍夫的分类的可能子群的有限交换群，并以不变的子空间问题的算子理论;并在重要例子中计算了子模嵌入范畴的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费尔德大学研究人员之间现有的合作。 它的成功将提高在东南部佛罗里达数学研究和研究生学习的机会。