"Burnside rings of profinite groups".

伯恩赛德环长期以来一直在有限群的背景下进行研究和应用，并在有限群表示理论中发现了许多有用的应用。目前，对无限群表示理论感兴趣的群理论家忽视了Burnside环。本课题旨在为无限群的Burnside环及其变体和Mackey代数建立一个完善的理论框架，使我们能够获得新颖而重要的结果，并研究我们的理论在代数之外的应用。

The Burnside ring has long been investigated and used in the context of finite groups and it has found numerous useful applications in finite group representation theory.At present, Burnside rings have been overlooked by group theorists interested in representation theory of profinite groups. With the proposed project, we aim to create a sound theoretical framework of Burnside rings, its variants and Mackey algebras for profinite groups, which enables us to obtain original and important results, and investigate the applications of our theory beyond algebra too.