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I am interested in interactions between algebraic topology and representation theory. Through the apparatus of support varieties, group cohomology rings control a lot of the large scale structure in modular representation theory. Group cohomology rings are also objects of study in algebraic topology, so we can use topological techniques to ultimately say something about modular representation theory.
My thesis work was largely focused on using the Borel equivariant cohomology of smooth manifolds with a smooth elementary abelian p-group action to study the geometry of group cohomology rings, especially their local cohomology modules. I am currently working on a project that more directly relates these smooth manifolds to modular representation theory.
I am also interested in tensor triangulated geometry writ large, and in transporting ideas from modular representation theory to other tensor triangulated settings.
Publications and Preprints
- Computing homological residue fields in algebra and topology, joint with Paul Balmer, Proceedings of the American Mathematical Society, 149, no 8 (2021), pp. 3177-3185.
- On the Duflot filtration for equivariant cohomology rings, my thesis. This is essentially the same as the arxiv preprint listed below, except for an extra chapter on the derived category of cochains on the Borel construction of a smooth manifold.
- On the Duflot filtration for equivariant cohomology rings, Arxiv preprint.