Morgan Opie


Preprints

Enumerating corank 2 complex vector bundles on odd complex projective spaces , with Yang Hu (2026).
High-corank torsion in homotopy of unitary groups via topological modular forms and higher real K-theories, with Hood Chatham and Yang Hu. Submitted (2026).
Efficient generation of projective modules: a motivic view, with Aravind Asok, Brian Shin and Tariq Syed. Submitted (2025).
On algebraic vector bundles of rank 2 over smooth affine fourfolds, with Thomas Brazelton and Tariq Syed. Submitted (2025).
Enumerating stably trivial vector bundles with higher real K-theories, with Hood Chatham and Yang Hu. Submitted (2024).

Accepted and published papers

Enumerating complex rank n vector bundles on CP^{n+1}. To appear in Proc. AMS.
Rank-preserving additions for topological vector bundles, after a construction of Horrocks. Algebraic & Geometric Topology (2025).
Cofibration category of digraphs for path homology, with Daniel Carranza, Brandon Doherty, Chris Kapulkin, Maru Sarazola, and Liang Ze Wong. Algebraic Combinatorics (2024).
A classification of complex rank 3 bundles on complex projective 5-space. Advances in Mathematics (2024).
Compactly Supported A^1-Euler characteristic and the Hochschild complex, with Niny Arcila Maya, Candace Bethea, Kirsten Wickelgren, and Inna Zhakarevich. Topology and its Applications (2022).
The trace of the A^1-local degree, with Thomas Brazelton, Robert Burklund, Stephen McKean, and Michael Montoro. Homotopy, Homology, and Applications (2021).
Localization in Homotopy Type Theory, with J. Daniel Christensen, Egbert Rijke and Luis Scoccola. Higher Structures (2020).
Effective divisors on moduli spaces of rational curves with marked points. Michigan Math. J. (2016)

Other work

As part of my undergrad thesis, I created a related database of spherical hypertree divisors generated using Macaulay2.