Derived categories and their many applications

该项目旨在解决代数中的主要开放问题，以解决已经存在数十年的问题。这项拟议中的研究是开创性的，为困扰世界各地专家的问题引入了新方法。该项目计划使用的技术来自同调代数，更具体地说，来自派生类别。使用新方法的初步工作已经在以前已知的基础上取得了重大进展。该项目雄心勃勃：如果真的成功，希望能重塑这一主题，加深我们对这一领域的理解，但即使是更小的成就，也有望澄清和改进国际专家40年来的工作。

This project aims to work on major open problems in algebra, towards the solution of conjectures that have been around for decades. The proposed research is ground-breaking, introducing new methods to problems that have stumped experts around the world. The planned techniques the project will use come from homological algebra, more specifically, from derived categories. Preliminary work, using the new methods, has already led to major advances on what was previously known. The project is ambitious: if really successful, it is hoped to reshape the subject and deepen our understanding of the field, but even more modest achievements are expected to clarify and improve on work by international experts over four decades.