# Eric G. Samperton

## Teaching

During the fall 2019 semester, I am teaching MATH 213. Here is the course webpage.

## About me

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.

## Writing

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.

## Contact Information

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