I am a PhD candidate at the University of Toronto working under Ragnar-Olaf Buchweitz. I work on commutative algebra and the representation theory of algebras, using ideas from algebraic topology. The general theme in most of what I'm interested in is Koszul duality.
Specifically, I think about: triangulated categories and support theory; singularity categories and stable module categories; the structure of Hochschild cohomology; and Koszul duality using homotopy coherent algebraic structures.
Recently I have been thinking a lot about local commutative algebra. Especially the homotopy Lie algebra and André-Quillen cohomology. Koszul duality here takes the form of an unexpectedly wide-reaching analogy with rational homotopy theory.
I am also co-organising the Homological Methods Seminar at Toronto. This year we are focusing on the representation theory that goes in to categorifying the combinatorics of cluster algebras. Email me if you would like to be involved.
ben dot briggs at mail dot utoronto dot ca