Derived categories and their applications, especially in K-theory, topology and algebraic geometry

代数几何、拓扑学和代数K-理论是研究几何不同方面的数学学科。在所有这些研究领域中，派生类别已被证明是强大的工具。这个项目的目的是使用派生类别来提高我们对几何的理解。所涉及的是20世纪下半叶以来几何学中的一些主要开放问题。 这项研究被提名为复杂/智能系统优先领域。几何在两个方面都是相关的。安全和/或纠错码通常基于代数几何。对并发问题进行建模涉及到同伦理论。

Algebraic geometry, topology and algebraic K-theory are mathematical disciplines that study different aspects of geometry. In all these areas of study, derived categories have proved to be powerful tools. This project aims to use derived categories to advance our understanding of geometry. Involved are some of the main open questions in geometry from the second half of the twentieth century. The research is being nominated for the Complex/Intelligent Systems Priority Area. Geometry is relevant in two ways. Secure and/or error correcting codes are often based on algebraic geometry. And modelling concurrency problems involves homotopy theory.