During the spring 2020 semester, I am teaching MATH 417. Here is the course webpage.

I am a J. L. Doob Research Assistant Professor in the University of Illinois Math Department. Recently, I was a visiting professor at UC Santa Barbara, and earned my Ph.D. from UC Davis. My advisor was Greg Kuperberg.

My primary motivation is to answer questions at the intersection of 3-manifold topology and computational complexity. Broadly, I do research in overlaps of the following subjects:

- (Low-dimensional) geometric topology
- Geometric group theory
- Computational complexity
- Topological quantum field theory
- Quantum computing and quantum information
- Topological condensed matter theory

To be clear, I'm not a physicist or computer scientist. I am more interested in applying ideas from these fields to better understand topology and TQFT. (Although occasionally—to Hardy's dismay—the arrow of ideas points in both directions.) For example, I have used ideas inspired by topological quantum computing to prove complexity-theoretic lower bounds for problems in 3-manifold topology.

Here's my CV. Here's a very full, loose lamination with \(\mathbb{Z}/4 * \mathbb{Z}/3\) symmetry:

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

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

**(6)** **Coloring invariants of knots and links are often intractable.** With Greg Kuperberg. Submitted. arXiv Front.

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

**(4)** **Schur-type invariants of branched G-covers of surfaces.** To appear in Proceedings of the AMS Special Session on Topological Phases of Matter and Quantum Computation. arXiv Front.

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

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

**(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 Front.

My Ph.D. dissertation is titled **Computational Complexity of Enumerative 3-Manifold Invariants** and can be found at the arXiv Front or ProQuest. It contains the results of items **(3)**, **(4)** and **(6)** above.

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

Office: 247B Illini Hall

Snail Mail:

Department of Mathematics

1409 West Green Street (MC-382)

Urbana, IL 61801