This page contains information about my mathematics research. Comments and questions welcome. Versions on my arxiv page may be slightly out of date.

**Wonderful asymptotics of matrix coefficients \(\mathcal{D}\)-modules**

With D. Ben-Zvi. *Advances in Mathematics*, Volume 408, Part A (2022).

**The quantum Frobenius for character varieties and multiplicative quiver varieties**

With D. Jordan and P. Safronov. *Journal of the European Mathematical Society*, forthcoming.

**Quantum Weyl algebras and reflection equation algebras at a root of unity.** With N. Cooney and D. Jordan. *Journal of Pure and Applied Algebra,* Volume 224, Issue 12 (2020).

**The wonderful compactification for quantum groups**

*Journal of the London Mathematical Society,* Volume 99, Issue 3 (2019), Pages 778–806.

** Quantizations of multiplicative hypertoric varieties at a root of unity.
**

*Journal of Algebra*, Volume 506 (2018), Pages 92–128.

**Groups of a square-free order**.

*Rose-Hulman Undergraduate Math. Journal*, Vol. 11, Issue 1 (2010).

**Order dimension of subgroups**.

*Rose-Hulman Undergraduate Math. Journal*, Vol. 9, Issue 2 (2008).

**The wonderful compactification for quantum groups.**

University of Texas at Austin, 2016.

Below is a collection of expository notes on various topics in geometric representation theory. The notes are grouped by theme, and within each theme are roughly ordered from most accessible to most specialized.

Many of these notes are from talks given at learning seminars, summer schools, workshops, etc. They are informal and may contain mistakes. Use at your own risk! Corrections are welcome.

**A glimpse into geometric representation theory**. Think and Drink Seminar, IST Austria, May 2019. [pdf]**Young tableaux, symmetric polynomials, and representations**. UT Austin Math Club, February 2012. [pdf]**Representations of finite groups**. Categorical representation theory workshop, University of Oregon, August 2012. [pdf]**Real and quaternionic representations of finite groups**. December 2011. [pdf]**SU(2) as a double cover of SO(3) and related topics**. December 2011. [pdf]**An overview of Springer theory**. Geometry learning seminar, UT Austin, November 2012. [pdf]**The derived category of constructible sheaves.**With Robin Walters. Summer school on quiver Hecke algebras, IESC, Corsica, June 2014. [pdf]**Tannaka duality for affine group schemes.**Candidacy Talk, September 2012. [pdf]

**An introduction to character sheaves**. Geometry learning seminar, UT Austin, October 2013. [pdf]**Unipotent characters of finite groups of Lie type**. Geomtery learning seminar, UT Austin, April 2013. [pdf]**Lusztig's non-abelian Fourier transform**. April 2019. [pdf]-
**The Radon transform**. May 2019. [pdf]

**Quantum \(\mathfrak{sl}_2\)**. Algebraic geometry working seminar, IST Austria, April 2018. [pdf]**Quantum Hamiltonian reduction**. December 2013. [pdf]**Quasi-bialgebras and associators**. Workshop on quantization and formality, UT Austin, June 2014. [pdf]**Quantum multiplicative quiver varieties at a root of unity**. Mathematics and String Theory Seminar, Kavli IPMU, June 2019. [pdf]