Assistant Professor

Departments of Mathematics and Computer Science

Purdue University

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).

**(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:

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

In the fall 2024 semester, I will be teaching MA 562 - Introduction to Differential Topology and Geometry. If you're wondering, the textbook we'll be using is Lee's Introduction to Smooth Manifolds (GTM 218). Check back later for more info, or send me an email if you have questions.

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

- Spring 2023: CS 59300/MA 59500 - Introduction to Quantum Computation
- Spring 2021 (at UIUC): MATH 595 - Quantum, Complexity, and Topology

**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