My research area is geometric representation theory. I am interested in quantizations of multiplicative hypertoric and multiplicative quiver varieties, especially at roots of unity, as instances of the general framework of Frobenius quantum moment maps. I am also thinking about the wonderful compactification and applications to quantum geometric representation theory. Another interest is deformations of category O for rational Cherednik algebras and relations to sheaves on moment graphs.
Preprint: Quanitzations of multiplicative hypertoric varieties. arXiv:1412.7211
Working group on the geometric Satake equivalence, MSRI, Fall 2014.
Workshop on Yangians and quantum loop algebras, near Austin, May 2014.
Learning seminar on categorical representation theory related topics, UT Austin, Spring 2012 and part of Summer 2012.
Here are a few talks I have presented:
- The symmetric monoidal structure on the Satake category.
Working group on the Geometric Satake Equivalence, MSRI, November 2014.
- Quantum multiplicative hypertoric varieties at a root of unity.
University of California, Berkeley, September 2014.
AMS section meeting, Lubbock, TX, April 2014.
University of Edinburgh, March 2014.
GADGET seminar, UT Austin, February 2014.
- The derived category of constructible sheaves. (Joint with Robin Walters, notes)
Summer school on Quiver Hecke algebras (link).
Institut d'Études Scientifiques de Cargèse Corsica, June 2014.
- Quasi-bialgebras and associators. (Notes)
Workshop on quantization and formality (link), UT Austin, June 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, some of which are relatively informal:
- Torus-valued moment maps (pdf)
- Quantum Hamiltonian reduction (pdf)
- 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 when I worked in a biology lab.