Nicolas Bridges

Ph.D. Candidate

Department of Mathematics
Purdue University

150 N. University Street
West Lafayette, Indiana 47907

Office: Math 641
Email: bridge18 at purdue dot edu

My CV

Student Quantum Topology Seminar

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

Teaching

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

Research Interests

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

Papers (Reverse chronological order)

(1) Towards a complexity-theoretic dichotomy for (2+1)-dimensional TQFT invariants. With Eric Samperton. Preprint https://doi.org/10.48550/arXiv.2503.02945

(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. In progress.

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