James Maxwell
Personal Information
I have a post-doc position as a Heilbronn Reseach Fellow (Oct 2022 - Sept 2024) in the School of Mathematics at the University of Bristol, under the mentorship of Farhad Babaee.
My research will be continuing in the areas that my PhD was based.
Research Interests
My research interests include tropical geometry, algebraic geometry and hyperfields. During my PhD the aim has been to understand how results from classical algebraic geometry and tropical geometry hold over hypefields. This has so far had a particular focus on Kapranov's Theorem.
In the last year I have been exploring how convex geometry can be studied over ordered hyperfields with Ben Smith.
I am also interested in tropical ideals, in the sense of MRa and MRb. In particular, when the geometric objects defined by tropical ideals should be considered equivalent.
My broader interests include; algebraic and tropical combinatorics, polyhedral geometry and matroid theory.
Research
Publications
J.Maxwell, Generalising Kapranov's Theorem for Tropical Geometry over Hyperfields, Journal of Algebra (https://www.sciencedirect.com/science/article/pii/S002186932300474X), (arXiv version https://arxiv.org/abs/2108.01524).
Preprints
J.Maxwell & B.Smith, Convex Geometry over Ordered Hyperfields (arXiv:2301.12760).
J.Maxwell & B.Smith, Geometry of tropical extensions of hyperfields (arXiv:2309.17302).
F.Babaee, S.Dewar & J.Maxwell, Extremal decompositions of tropical varieties and relations with rigidity theory (arXiv:2403.00655).
Projects
J.Giansiracusa & J.Maxwell, Abstract Varieties for Tropical Ideals (In Progress).
Contact Information
Email: james (dot) maxwell (at) bristol.ac.uk
Email: james.william.maxwell (at) gmail.com
Office: 2.11, School Of Mathematics, Fry Building, University of Bristol.
Previous Contact Details
Email: 825537@swansea.ac.uk (Terminated July 2022)
Email: j.w.maxwell@swansea.ac.uk (Terminated July 2022)
Educational Background
PhD (Passed September 2022):
I studied for my PhD at Swansea Univerisity, under the supervision of Prof Jeffrey Giansiracusa (Durham) and Dr Edwin Beggs. The work was focused on the generalisations of key results from tropical geometry to the multivalued setting of hyper structures.
See my thesis here: https://cronfa.swan.ac.uk/Record/cronfa61752. The work from several sections is currently being continued and will be published as individual articles in the near future.
MSc: Mathematics (Distinction), Swansea University. I reviewed Kapranov's Theorem and the Fundamental Theorem of Tropical Geometry in my Masters Dissertation. Then I started to explore generalisations of results from Tropical Geometry to Hyperfield structures. This work has continued into my PhD studies.
BSc: Mathematics and Sports Science (Hons, 1st), Swansea University.