Homological methods in combinatorics, algebra and geometry

这个项目的目的是用代数技术解决图论、格论和几何中的问题。这种代数方法提供的技术和语言将被用来获得对经典问题的新见解，证明更强大的定理，并揭示不同领域之间的联系。该项目旨在将澳大利亚在同调代数和范畴理论方面的优势与在不同数学领域的应用相结合。预计这将为进一步研究其他领域的应用提供工具，包括计算机科学和组合优化。

This project aims to solve problems in graph theory, lattice theory and geometry using algebraic techniques. The techniques and language provided by this algebraic approach will be used to gain fresh insight into classical problems, prove stronger theorems and uncover connections between different areas. This project intends to integrate Australia’s strength in homological algebra and category theory with applications in various different fields of mathematics. This is expected to provide tools for further investigation of applications in other fields, including computer science and combinatorial optimisation.