Derived categories and their many applications

这个项目的目的是致力于解决代数中的主要公开问题，解决几十年来一直存在的猜想。这项拟议的研究具有开创性，为困扰世界各地专家的问题引入了新的方法。该项目将使用的计划技术来自同调代数，更具体地说，来自派生类别。使用新方法的初步工作已经在先前已知的基础上取得了重大进展。该项目是雄心勃勃的：如果真的成功，它有望重塑这一主题，加深我们对该领域的理解，但预计更温和的成就将澄清和改进国际专家在过去40年里所做的工作。

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.