I am a Simons Postdoctoral Fellow at the Hamilton Mathematics Institute, affiliated with Trinity College Dublin. I obtained my PhD at the University of Toronto in August 2018, where I was advised by Ragnar-Olaf Buchweitz, Colin Ingalls and Joel Kamnitzer. My thesis was titled 'Contributions to the Stable Derived Categories of Gorenstein Rings'.
I am interested in homological/homotopical algebra, commutative algebra, algebraic geometry (classical and noncommutative) and representation theory of algebras. Lately, my research interests have revolved around the following:
- triangulated categories, principally the structure of singularity categories and derived categories of coherent sheaves;
- Koszul duality and A-infinity structures;
- Hochschild cohomology and support varieties;
- tilting theory, exceptional collections and their applications;
- the structure of higher preprojective algebras, Artin-Schelter regular algebras and graded algebras associated to geometric helices.
Work in preparation
- Formulas for A-infinity universal envelopes and Ext algebras of commutative rings, joint with Ben Briggs.
- Classification of standard graded complete intersections admitting a tilting object.
- The BGG correspondence for absolutely Koszul Gorenstein rings, with applications to conjectures of Bondal and Minamoto.
The last two points are extensions of chapters 2,4,5,6 of my thesis. A copy can be obtained on T-space
, or directly