Homological methods in combinatorics, algebra and geometry

This mathematical project aims to solve problems in graph theory, lattice theory, and geometry using a novel combination of algebraic techniques. The new techniques and language provided by this algebraic approach will be used to gain fresh insight into classical problems, prove stronger theorems and uncover novel connections between different areas. Homological algebra and category theory is a strength of Australian mathematics, and the intended outcome of the project is to integrate this existing strength with applications in various different fields of mathematics. This will provide tools for further investigation of applications in other fields, including computer science and combinatorial optimisation.