Mathematical Sciences: Invariants and Endomorphisms of Groups and Modules

该奖项将支持对各种有限可数秩无扭阿贝尔群结构的研究。根据传统的Baer和Ulm不变量，将Butler群的类划分到（拟或近）同构。代数其他领域的各种应用，如有限偏置集的表示和多个回拉环上的有限生成模块也将被考虑。本课题属于阿贝尔群论的一般领域，涉及阿贝尔群的分类。虽然有限阿贝尔群的分类已经被很好地理解了一个世纪，无限阿贝尔群的分类仍然是难以捉摸的。本研究涉及到用逻辑学和分析学的新工具来解决无穷阿贝尔群的分类这一老问题。

This award will support the study of the structure of various classes of finite and countable rank torsion-free abelian groups. Classes of Butler groups will be classified up to (quasi or near)-isomorphism by invariants in the tradition of Baer and Ulm invariants. Various applications to other areas of algebra, such as representations of finite posets and finitely generated modules over multiple pullback rings will also be considered. This project is in the general area of abelian group theory and is concerned with the classification of abelian groups. Although the classification of finite abelian groups has been well understood for a century, the classification of infinite abelian groups remains elusive. This research involves this old problem of classification of the infinite abelian groups approached by new tools from logic and analysis.