Research

My research interests focus on algebraic groups, representation theory, and related algebraic geometry; broadly, the connections and interactions between algebra and geometry.

I am particularly interested in the geometry of certain special varieties which arise in the study of representations of algebraic groups. These special varieties include Schubert varieties, nilpotent orbits, orbital varieties, and support varieties.

I’ve been programming computers since I was small. Lately I’m into Python and Haskell. During the day I’m a research engineer at Galois, Inc. (the worlds largest Haskell shop). I’m also a developer on the Sage mathematical software project and a troll on Ask Sagemath.

Publications

(listed in reverse chronological order)

  1. On the Structure of Involutions and Symmetric Spaces of Dihedral Groups

co-authors: T. J. Edgar, A. G. Helminck, et. al.
submitted for publication (2012)
preprint

  1. On the Support Varieties of Demazure Modules

co-author Daniel Nakano
J. Aust. Math. Soc. 91 (2011), 343 – 363
doi:10.1017/S144678871100173X
preprint

  1. First cohomology for finite groups of Lie type: simple modules with small dominant weights

co-authors UGA VIGRE Algebra Group
to appear in Transactions of the American Mathematical Society
preprint

  1. Normality of orbit closures in the enhanced nilpotent cone

co-authors Pramod Achar and Anthony Henderson
Nagoya Math. J. 203 (2011), 1–45
preprint

  1. Singular Chern Classes of Schubert Varieties via Small Resolution

Int. Math. Res. Notices 8 (2010) 1371–1416
doi: 10.1093/imrn/rnp174

  1. An analog of Kostant’s theorem for the cohomology of quantum groups

co-authors UGA VIGRE Algebra Group
Proc. Amer. Math. Soc. 138 (2010), 85–99
PDF

Miscellaneous

A list of all my articles on the math preprint arXiv } My Ph.D. Thesis

Computational Projects

My computational projects are hosted on github.com.