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About me

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.

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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

(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. 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:

• Juan Alonso
• Andrés Ángel
• Harry Baik
• Colleen Delaney
• Greg Kuperberg
• Clément Maria
• Carlos Segovia
• Bernardo Uribe
• Zhenghan Wang

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Teaching

In the spring of 2024, I am teaching CS 59300/MA 59500 - Introduction to Quantum Computation and also MA 265 - Intro to Linear Algebra.

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.

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Contact Information

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

Office: Mathematical Sciences Building 402

Snail Mail:

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