Departments of Mathematics and Computer Science
My research focuses on interactions between topology and computer science. I am most interested in 3-dimensional geometric topology and topological quantum field theories, topological quantum computation, quantum and classical algorithms, and complexity.
Here is my CV.
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).
(9) Topological quantum computation is hyperbolic. Communications in Mathematical Physics (2023). arXiv
(8) Oriented and unitary equivariant bordism of surfaces. With Andrés Ángel, Carlos Segovia and Bernardo Uribe. Accepted for publication in Algebraic & Geometric Topology. 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:
During the spring of 2023 I am teaching Sections 213 and 214 of MA 26500 - Linear Algebra. Please login to Brightspace to access all of the course info.
In the spring of 2021, I taught MATH 595 - Quantum, Complexity, and Topology at the University of Illinois. If you want to watch the videos for this class you can find them available for public view at the Illinois Media Space channel here.
E-mail: my first name followed by @purdue.edu
Office: Mathematical Sciences Building 402
150 N University St
West Lafayette, IN 47907