I am a J. L. Doob Research Assistant Professor in the University of Illinois Math Department and a member of the Illinois Quantum Information Science and Technology Center (IQUIST). Recently, I was a visiting professor at UC Santa Barbara, and before that I earned my Ph.D. from UC Davis, where my advisor was Greg Kuperberg. I am partly supported by NSF grant DMS #2038020.

Beginning in August 2022, I will be an assistant professor at Purdue University in the departments of mathematics and computer science.

I study topology, and am especially focused on answering questions about the computational complexity of 3-dimensional manifolds and their quantum algebraic invariants. My work involves methods and ideas from various subjects, including:

- (Low-dimensional) geometric topology
- Finite and geometric group theory
- Computational complexity
- Topological quantum field theory (TQFT) and quantum algebra
- Quantum computation/information/algorithms
- Topological condensed matter theory

Here's my CV. And just for fun, here's a very full, loose lamination with \(\mathbb{Z}/4 * \mathbb{Z}/3\) symmetry that was used in the paper **(1)** below:

My papers and preprints are listed below, along with links to published versions and arXiv preprints. You might also want to check out my arXiv author page, my MathSciNet author profile (subscription required) or my Google Scholar profile.

**(9)** **Topological quantum computation is hyperbolic.** Submitted. arXiv

**(8)** **Oriented and unitary equivariant bordism of surfaces.** With Andrés Ángel, Carlos Segovia and Bernardo Uribe. Submitted. arXiv

**(7)** **Free actions on surfaces that do not extend to arbitrary actions on 3-manifolds.** Comptes Rendus - Mathématique (2022), Volume 360, pp. 161-167. arXiv

**(6)** **Coloring invariants of knots and links are often intractable.** With Greg Kuperberg. Algebraic & Geometric Topology (2021), Volume 21, Issue 3, pp. 1479-1510. arXiv

**(5)** **Haah codes on general three manifolds.** With Kevin Tian and Zhenghan Wang. Annals of Physics (2020), Volume 412, 168014. arXiv

**(4)** **Schur-type invariants of branched G-covers of surfaces.** Topological Phases of Matter and Quantum Computation (2020), *Contemp. Math.*, Volume 747, pp.173-197. arXiv

**(3)** **Computational complexity and 3-manifolds and zombies.** With Greg Kuperberg.
Geometry & Topology (2018), Volume 22, Issue 6, pp. 3623-3670. arXiv

**(2)** **Spaces of invariant circular orders of groups.** With Harry Baik. Groups, Geometry, and Dynamics (2018), Volume 12, Issue 2, pp. 721-763. arXiv

**(1)** **On laminar groups, Tits alternatives, and convergence group actions on \(S^2\).** With Juan Alonso and Harry Baik.
Journal of Group Theory (2019), Volume 22, Issue 3, pp. 359-381. arXiv

My Ph.D. dissertation is titled **Computational Complexity of Enumerative 3-Manifold Invariants** and can be found at the arXiv or ProQuest. It more-or-less contains the results of items **(3)** and **(6)** above.

Here are links to most of my co-authors' webpages:

Here's a video of a talk I gave at the University of Warwick related to my dissertation: YouTube.

Here's a more recent talk I gave at CLAM VI related to my paper **(7)** above: YouTube.

I am not teaching during the spring 2022 semester. In the spring of 2021, I taught MATH 595 - Quantum, Complexity, and Topology. If you want to watch the videos for the latter class you can find them available for public view at the Illinois Media Space channel here.

E-mail: My last name without any vowels, followed by @illinois.edu

Office: 257C Altgeld Hall

Snail Mail:

Department of Mathematics

1409 West Green Street (MC-382)

Urbana, IL 61801