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衍生类别来推进我们对几何的理解。本书涉及到二十世纪下半叶几何学中一些主要的开放性问题。

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.