I am a visiting assistant professor in the UC Santa Barbara Math Department. I recently earned my Ph.D. from the Math Department at 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.

I am a co-organizer of the UCSB Quantum Algebra and Topology Seminar, which usually meets Tuesdays at 11AM.

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 (login required) or my Google Scholar profile.

**(6)** **Coloring invariants of knots are often intractable.** With Greg Kuperberg. In preparation.

**(5)** **Haah codes on general three manifolds.** With Kevin Tian and Zhenghan Wang. Submitted. 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. 721-76. arXiv Front.

**(1)** **On laminar groups, Tits alternatives, and convergence group actions on \(S^2\).** With Juan Alonso and Harry Baik. Available ahead of print in Journal of Group Theory. 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 first name followed by @math.ucsb.edu

Office: 6702 South Hall

Snail Mail:

Department of Mathematics

South Hall, Room 6607

University of California

Santa Barbara, CA 93106-3080