My research area is geometric representation theory. My advisor is David Ben-Zvi.
One of my current research projects involves a quantization of hypertoric varieties. The quantization features a certain algebra of q-difference operators on affine space. When q is a root of unity, this algebra gives rise to an Azumaya algebra on the muliplicative hypertoric variety, via a Hamiltonian reduction procedure. We are currently working on a localization theorem and on conditions for finite homological dimension. Various aspects of this work are joint with or guided by David Jordan, Nicholas Cooney, and Kobi Kremnitzer. Please email me if you would like to see a draft of this work.
I co-organized a workshop on Yangians and quantum loop algebras, which was held near Austin in May 2014.
During Spring 2012 and part of Summer 2012, I co-organized a learning seminar on categorical representation theory related topics.
Here are a few talks I have presented:
- Quasi-bialgebras and associators. (Notes)
Workshop on quantization and formality (link), UT Austin, June 2014.
- Quantized multiplicative hypertoric varieties.
University of Edinburgh, March 2014.
- An introduction to character sheaves. (Notes)
Student Geometry Seminar, October 2013.
- Unipotent characters of finite groups of Lie type. (Notes)
Student Geometry Seminar, April 2013.
- Deformation theory. (Notes)
Ben-Zvi Seminar, March 2013.
- Geometric realizations of affine Hecke algebras.
RTG Geometry and Topology Current Literature Seminar, January 2013.
- An overview of Springer theory.
Student Geometry Seminar, November 2012. (Notes)
Ben-Zvi Seminar, October 2012. (Two lectures, notes from part 2)
- Tannaka duality for affine group schemes. (Notes)
Candidacy Talk, September 2012
- Representations of finite groups. (Notes)
Categorical Representation Theory Workshop (link)
Eugene, Oregon, August 2012
- Young tableaux, symmetric polynomials, and representations. (Notes)
Undergraduate Math Club, February 2012. A video can be found here.
In addition to the notes above, here are some other things I have written:
- Real and quaternionic representations of finite groups. (pdf)
- SU(2) as a double cover of SO(3) and related topics. (pdf)
- Undergraduate project: Groups of square-free order. (pdf)
- A research paper from the days when I worked in a biology lab.