I am a Member of the Institute for Advanced Study's School of Mathematics.
Before then, I was a Postdoctoral Research Fellow at the University of British Columbia's Department of Mathematics.
I am interested in algebraic geometry and geometric representation theory, focusing on new approaches to understanding
categories of coherent sheaves and D-modules. In particular, my current projects include:
- giving new characterizations of perverse coherent and exotic sheaves, with regards to their microlocal nature and interactions with geometric Lie algebra actions;
- exploiting the new characterizations to generalize these theories;
- computations of Hochschild cohomology of categories of D-modules;
- understanding cohomological support of D-modules on stacks of representation theoretic interest;
- D-modules in log geometry and their application to representation theory.
Publications & Preprints
My thesis, Some microlocal aspects of perverse coherent sheaves and equivariant D-modules.
- Holonomic and perverse logarithmic D-modules, with Mattia Talpo [arXiv]
- Exotic t-structures and actions of quantum affine algebras, with Sabin Cautis. To appear in the Journal of the European Mathematical Society. [arXiv]
- Hochschild cohomology of torus-equivariant D-modules. To appear in IMRN. [arXiv]
- Exact functors on perverse coherent sheaves. Compositio Mathematica 151 (2015), no. 9 [DOI] [arXiv]
- Exotic sheaves and actions of quantum affine algebras, Hausdorff Institute for Mathematics, November 2017 [Poster PDF] [Talk PDF]
- Categorical actions in geometry and representation theory, Institute for Advanced Study, September 2017 [PDF]
- Exotic sheaves and actions of quantum affine algebras, Poster at Interactions between Representation Theory and Algebraic Geometry, Chicago, August 2017 [PDF]