Peter Brooksbank
Professor of Mathematics
Bucknell University
Welcome!
I am a mathematician at Bucknell University — 'Ray Bucknell! When not teaching or doing math, I enjoy my friends, cycling, coffee, reading, squash, walking my dogs, and watching Liverpool (not so much this season).
Research Interests
Here are my primary research areas:- Group Theory
- Algebraic Algorithms
- Tensors
- Discrete Geometry
Teaching
In Spring 2026 I am teaching Multivariable Calculus.If you are a Bucknell student interested in data science research this summer, the Summer Research Program at The Dominguez Center for Data Science has some great opportunities. If you have some background in linear algebra, are interested in computation, and would like to work in my team on tensor research, you can apply here.
News & Updates
- [Feb 2026] An update of my preprint with Martin Kassabov and James Wilson on Detecting sparsity patterns in tensor data is available on arXiv.
- [Jan 2026] The paper Categorification of characteristic structures coauthored with Heiko Dietrich, Eamonn O'Brien, Joshua Maglione, and James Wilson has appeared in Forum of Mathematics, Sigma.
- [Nov 2025] A preprint on New linear invariants of hypergraphs coauthored with Clara Chaplin is available on arXiv.
- [Oct 2025] An implementation of abstract categories in Agda is available from a public GitHib repository: Glassbox represents a first step in realizing categorification of characteristic structure in algebras.
Selected Recent Publications
- PAB, H. Dietrich, J. Maglione, E.A. O'Brien, J.B. Wilson, Categorification of characteristic structures, Forum of Mathematics, Sigma, 14 (2026).
- PAB, J. Maglione, J.B. Wilson, Tensor isomorphism by conjugacy of Lie algebras, Journal of Algebra 604 (2022), 790—807.
- PAB, J.T. Ferrara, D. Leemans, Orthogonal groups acting on polytopes of high rank, Discrete and Computational Geometry 63 (2020), 656—669.
- PAB, J. Maglione, J.B. Wilson, Exact sequences of inner automorphisms of tensors, Journal of Algebra 545 (2020), 43—63.
- PAB, E.A. O'Brien, J.B. Wilson, Testing isomorphism of graded algebras, Transactions of the American Mathematical Society 372 (2019), 8067—8090.
- PAB, D. Leemans, Rank reduction of string C-group representations, Proceedings of the American Mathematical Society 147 (2019), 5421—5426.