I am a third-year graduate student in mathematics at MIT studying geometric representation theory. My advisor is Roman Bezrukavnikov.
Equivariant coherent sheaves on the exotic nilpotent cone, (preprint). (arXiv)
Let G be the symplectic group, and consider Kato's exotic nilpotent cone. Following techniques used by Bezrukavnikov to establish a bijection between the dominant weights for a simple algebraic group, and O, the set of pairs consisting of a nilpotent orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit, we prove an analogous statement for the exotic nilpotent cone. In order to this, we construct a quasi-exceptional set generating the bounded derived category of equivariant coherent sheaves on the exotic nilpotent cone, such that the resulting t-structure coincides with the perverse coherent t-structure.
An introduction to nilpotent cones. (pdf)
My honors thesis at the University of Sydney, supervised by Anthony Henderson.
Exotic t-structures for two-block Springer fibres. (Slides)
A description of the irreducible objects in the heart of the exotic t-structure corresponding to a 2-block Springer fibre, for the Usyd Algebra Seminar (in July, 2012).
Gelfand-Tsetlin bases and crystals. (pdf)
An exposition of the theory of Gelfand-Tsetlin bases and crystal, for this seminar.
Cluster algebras, and representations of quantum affine algebras. (pdf)
An exposition of some work by Hernandez and Leclerc which constructs a monoidal categorification of cluster algebras of finite type via a certain subcategory of representations of the quantum affine algebras, for this seminar.