Nicolas Bridges

I am currently hosting a student seminar in quantum topology. The website and schedule can be found here

Current Teaching (Spring 2025)

I am currectly teaching Mathematics for Elementary School Teachers I (MA 13700)

Past Teaching

• Fall 2023 and Spring 2024/25: MA 13700 - Mathematics for Elementary School Teachers I
• Fall 2022: MA 16010 - Applied Calculus I
• Spring 2022: MA 26200 - Linear Algebra and Differential Equations (TA)
• Fall 2021: MA 16200 - Calculus 2 (TA)

Research Interests

Quantum topology, quantum computing, Hopf algebras, topological quantum field theory, fusion categories, low dimensional topology, complexity theory

Papers (Reverse chronological order)

(1) Towards a complexity-theoretic dichotomy for (2+1)-dimensional TQFT invariants. With Eric Samperton. https://doi.org/10.4230/LIPIcs.TQC.2025.5 Leibniz International Proceedings in Informatics (LIPIcs), Volume 350, pp. 5:1-5:21

(2) Involutory Hopf group-coalgebras and invariants of flat bundles over 4-manifolds. With Shawn Cui. Preprint https://doi.org/10.48550/arXiv.2503.08861

(3) Invariants from involutory Hopf algebras of 3-manifolds with embedded framed links. With Shawn Cui. Preprint https://doi.org/10.48550/arXiv.2509.07125

(4) Anomalous branch locus defects in homotopy quantum field theories. With Eric Samperton. In progress.

(5) Invariants of crossed-module-bundles over 4-manifolds from involutory Hopf crossed-module-coalgebras With Shawn Cui. In progress.