Groupoids as bridges between algebra and analysis

这个纯数学项目的重点是抽象代数和称为算子代数的泛函分析领域之间的相互作用。具体地说，它打算处理图C*-代数和莱维特路径代数的推广。在过去的十年里，研究人员发现了这些领域之间惊人的相似性，但没有统一的结果可以让他们系统地将技术和定理从一个领域转移到另一个领域。最近的研究表明，代数和C*-代数的群类群模型可能提供了缺失的环节。本项目旨在确定群类群在这两种理论中的作用，并分析和利用抽象代数和算子代数之间的协同作用。

This pure mathematics project focuses on the interplay between abstract algebra and the area of functional analysis known as operator algebras. Specifically, it is intended to deal with generalisations of graph C*-algebras and of Leavitt path algebras. Over the last decade, researchers have discovered striking similarities between these areas, but no unifying result that would allow them to transfer techniques and theorems systematically from one to the other. Recent research suggests that groupoid models for both algebras and C*-algebras may provide the missing link. This project aims to determine the role of groupoids in the two theories, and analyse and exploit the resulting synergies between abstract algebra and operator algebras.