Eric Samperton

About me

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:

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.


During the spring 2019 academic quarter, I am teaching MATH 4A - Linear Algebra with Applications. Please login to GauchoSpace to see the course website.

Contact Information

E-mail: My first name followed by

Office: 6702 South Hall

Snail Mail:
Department of Mathematics
South Hall, Room 6607
University of California
Santa Barbara, CA 93106-3080