The project produced fundamental research on Hochschild cohomology and related areas, and this research was disseminated at international conferences and workshops, and peer-reviewed and published in top quality journals.
One major achievement was a new relative theory of Koszul duality, developed in collaboration with Cameron, Letz, and Pollitz. This theory has many applications within commutative algebra and singularity theory, and made essential use of the tools developed earlier in the project. This work is currently under peer review. Another significant achievement is the development of the theory of proxy small objects. A preprint has been published on this work in collaboration with Iyengar and Stevenson. Following on from this work, significant new progress was made towards the growth problem for Hochschild cohomology in commutative algebra.
As another use of Hochschild cohomology in commutative algebra, the project greatly developed the theory of cohomological support varieties over a local ring in collaboration with Grifo and Pollitz. Many new results were proven using the theory developed earlier in the project, and these results have been peer reviewed and published in the Transactions of the American Mathematical society series B (the open access arm of Transactions of the American Mathematical society). The project also provided new fined-grained information on the Lie algebra structure of the first Hochschild cohomology group, in joint work with Rubio y Degrassi.
In a different direction, the project had applications to toric topology, revealing new links between cohomology operations on toric spaces and the commutative algebra of Stanley Reisner rings, and ultimately characterising equivariant formality of moment angle manifolds. This joint work with Amelotte has been peer reviewed and published in the Transactions of the American Mathematical society series B.
