I am post-doc in mathematics at the University of Utah working in
representation theory. Here is my CV and
my Research Statement.

**Equivariant coherent sheaves on the exotic nilpotent
cone**. pdf arxiv *
Represent. Theory 17 (2013), 663-681 *

Following techniques used by Bezrukavnikov to establish a bijection between the dominant weights for a simple algebraic group, and

**Exotic t-structures for two-block Springer fibers.**
(pre-print, joint w/ Rina Anno) pdf

Exotic
t-structures were introduced by Bezrukavnikov and Mirkovic in order to
study representations of Lie algebras in positive characteristic. Here
we study the exotic t-structure on *D _{n}*, the derived
category of coherent sheaves on a two-block Springer fibre (i.e. for a
nilpotent matrix of type

**Quiver varieties and crystals for symmetrizable
Kac-Moody algebras.** (pre-print, joint w/ Peter
Tingley) pdf

Kashiwara and Saito
constructed a geometric realization of the B(\infty) crystal for a
simply-laced Kac-Moody algebra, by using irreducible components of
Lusztig's quiver varieties (which are representation varieties of the
corresponding pre-projective algebra). We generalize this construction
to symmetrizable Kac-Moody algebras.

**Stability conditions for category O** (pre-print) pdf

Recently, Anno, Bezrukavnikov and Mirkovic have introduced
the notion of a real variation of stability conditions
(which is related to Bridgeland's stability conditions),
and construct an example using categories of coherent
sheaves on Springer fibers. Here we construct another
example, by studying certain sub-quotients of category O
with a fixed Gelfand-Kirillov dimension. We use the braid
group action on the derived category of category O, and
certain leading coefficient polynomials coming from
translation functors.

**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.