Eric Samperton

Assistant Professor
Departments of Mathematics and Computer Science
Purdue University


About me

My research mostly occurs at the intersection of geometric topology and theoretical computer science. I am especially interested in the interactions between low-dimensional topology and topological quantum field theories, quantum computation, and computational complexity theory. One overarching motivation is to understand the extent to which topology can help elucidate the two most important problems in quantum computing—namely, fault tolerance and quantum advantage. In a more "pure" math direction, I am also interested in the intrinsic computational complexity of various questions involving 3-dimensional manifolds.

Here is my CV.

Students and mentees

Current graduate students: Nicolas Bridges (co-advised with Shawn Cui)

Current postdoc: Gert Vercleyen (co-mentored with Colleen Delaney)

Research opportunities for current Purdue Ph.D. students. I have opportunities for both current math and CS graduate students at Purdue. Here is a sample of the types of problems that are on my mind these days:

These are generally pure math/theory projects. However, there are also opportunities of a more computational nature that would likely involve Gert Vercleyen and the Anyon Wiki.

Other ideas for projects are also welcome, especially if they have something to do with either quantum computing or geometric topology. Aside from my publications, you might peruse the old course materials for a class I taught called Quantum, Complexity, and Topology to get a flavor of the things that interest me. Potential students typically should have familiarity with at least two of the following at the graduate level: low-dimensional or algebraic topology, group theory, complexity theory, quantum computing or quantum mechanics.

Interested students are encouraged to reach out to me!

Note to prospective Purdue graduate students. As at most universities in the United States, Ph.D. applications at Purdue are handled by the departments, not individual professors. If you are interested in pursuing a math Ph.D., then apply here. If you are interested in pursuing a CS Ph.D., then apply here. In either application, you will have an opportunity to clearly indicate which Purdue faculty you are interested in working with. In particular, you do not need to email me if you are interested in studying at Purdue for a Ph.D. Moreover, if you send me an impersonal email vaguely asking about "Ph.D. opportunities," etc. that gives no indication you are specifically interested in working with me, then I will likely not reply.

Research opportunities for undergraduate students. I am looking for 2 or 3 undergraduate students to participate in the above projects. An ideal student will likely be an advanced math or CS major who possesses at least one of the following three sets of skills: significant programming experience, preferably involving either computational algebra or quantum computing; a firm grasp of both linear algebra and group theory and, preferably, some familiarity with topology or knot theory; or a firm grasp of quantum mechanics and the basic foundations of quantum computing, preferably including error-correction.

I hope to find these students by the end of the 2024 calendar year and do some directed reading/training during the spring 2025 semester. There is a good likelihood that these students can be paid as hourly researchers during the summer of 2025 (and possibly more in the future).

Interested students are encouraged to email me a copy of their resume/CV and a brief description of their interests and motivations. For related information, please read the REU opportunity announcement titled "Computational Quantum Algebra and the Anyon Wiki" on the Purdue Math REU Opportunities page.

In a slightly different direction, in the spring of 2025, I will also be running a project through the Purdue Experimental Math Lab. This is an entirely new program that the Math Department is piloting. You can see my project, among others, by clicking here and scrolling down.

Writing

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

(10) An algorithm for Tambara-Yamagami quantum invariants of 3-manifolds, parameterized by the first Betti number. With Colleen Delaney and Clément Maria. arXiv, Video

(9) Topological quantum computation is hyperbolic. Communications in Mathematical Physics (2023), Volume 402, pp. 79-96. arXiv, YouTube

(8) Oriented and unitary equivariant bordism of surfaces. With Andrés Ángel, Carlos Segovia and Bernardo Uribe. Algebraic & Geometric Topology (2024), Volume 24, Issue 3, pp. 1623-1654. 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, YouTube, accompanying code

(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, YouTube

(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 my co-authors' webpages:

Teaching

In the fall 2024 semester, I am teaching MA 562 - Introduction to Differential Topology and Geometry.

Here are a few classes I have taught in the past (along with course materials that you might find useful):

Contact information

E-mail: my first name followed by @purdue.edu

Office: Mathematical Sciences Building 706

Snail Mail:

150 N University St
Math Department
Purdue University
West Lafayette, IN 47907