Graded Symmetry in Algebra and Analysis

本专题将研究数学中的分次对称性，并将其建模为群胚和逆半群。广群在很长一段时间内一直是数学兴趣的中心，但近年来作为代数、分析和动力学的焦点而获得了特别的突出地位。大多数广群可以自然分次。该项目引入了群胚的分次组合不变量（如分次同调），并将它们与Steinberg和C*-代数对应物（如分次K-理论）联系起来。其结果是给抢手的统一不变量桥梁代数和分析，并用尽类群胚，这些更丰富的不变量将提供一个完整的分类。

This project will study graded symmetries in mathematics by modelling them as groupoids and inverse semigroups. Groupoids have been at the centre of mathematical interest for a long time, but have gained special prominence in recent years as a focal point for algebra, analysis and dynamics. The majority of groupoids can be naturally graded. The project introduces graded combinatorial invariants for groupoids (such as graded homology) and relates them to their Steinberg and C*-algebra counterparts (such as graded K-theory). The outcome is to give sought-after unified invariants bridging algebra and analysis, and to exhaust the class of groupoids for which these much richer invariants will furnish a complete classification.