Dr Jonathan Wilson
Jonathan currently teaches a variety of pure-based modules offered by the Mathematics BSc degree. His research, which is also rooted in pure mathematics, focuses on uncovering and exploiting connections between combinatorics, geometry, and representation theory. He is particularly interested in cluster algebras and their generalisations.
Jonathan leads modules across all three years of the Mathematics BSc degree, and offers a range of interdisciplinary final year projects. His research has gained international attention, and is published in world renowned journals such as Selecta Mathematica (New Series), International Mathematics Research Notices, and Discrete and Computational Geometry. In 2018 he was an invited speaker at the International Centre of Theoretical Sciences in Bengaluru, India. There he gave a three course lecture series for the School on Cluster Algebras.
Dr Wilson graduated with a PhD in Mathematics from Durham University in 2017; his research centred around cluster algebras and their relationship with surfaces. Following this he spent one year at University of Tübingen under the Teach@Tuebingen scheme, where, alongside research, he delivered a two semester graduate course on cluster algebras. Jonathan then held a DGAPA Postdoctoral Fellowship at National Autonomous University of Mexico, Mexico City. During this time, he significantly advanced the study of cluster structures on (triangulated) non-orientable surfaces. In a series of four papers he established various combinatorial frameworks for the theory; these fresh viewpoints uncovered a variety of fundamental results of the subject, and have formed the bedrock of further study. Jonathan is also actively applying these new techniques to the “classical” case of cluster algebras from orientable surfaces.
- PhD Mathematics, Durham University, 2017
- Master of Advanced Study (MASt) in Pure Mathematics, University of Cambridge, 2013
- BSc Mathematics, Swansea University, 2012
- Cluster algebras and their generalisations
- Orientable and non-orientable surfaces
- Representation theory of quivers
- Categorification of cluster algebras
- Combinatorial theory of polytopes
- Fellow of the Higher Education Academy, 2023
- Teach@Tübingen Award, Eberhard-Karls-Universität Tübingen, 2017–2018
- EPSRC Doctoral Scholarship, 2013–2017, Durham University
- Institute of Mathematics Prize, Institute of Mathematics and its Applications, 2011–2012
- Senior Foulkes Prize in Mathematics, Swansea University, 2011–2012
- Lynne Charles Prize in Mathematics, Swansea University, 2010–2011
- Junior Foulkes Prize in Mathematics, Swansea University, 2009–2010
Dr Wilson has significantly advanced the study of cluster structures on both (triangulated) orientable and non-orientable surfaces and. In a series of four papers he established various combinatorial frameworks for the non-orientable theory; these fresh viewpoints uncovered a variety of fundamental results of the subject, and have formed the bedrock of further study.
Since then, Jonathan has been actively applying these new techniques to the “classical” case of cluster algebras from orientable surfaces, and solved a long standing conjecture in the field. Indeed, in joint work with Prof Christof Geiss and Prof Daniel Labardini-Fragaso, he proved a deep connection between curves on surfaces and bases for the associated cluster algebras.
Key publications:
- (with Christof Geiß and Daniel Labardini-Fragoso) Bangle functions are the generic basis for cluster algebras from punctured surfaces with boundary, 2023, preprint: arXiv:2310.03306.
- (with Christof Geiß and Daniel Labardini-Fragoso) Laminations of punctured surfaces as τ-reduced irreducible components, 2023, preprint: arXiv:2308.00792.
- Surface cluster algebra expansion formulae via loop graphs, 2020, preprint: arXiv:2006.
- 13218, Laurent phenomenon algebras arising from surfaces II — laminated surfaces, Selecta Mathematica (New Series), 2020, preprint: arXiv:1802.06962.
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- Grant holder for the research group CLAN (Cluster Structures and their Applications in the North). This is an LMS funded joint research group between Durham, Glasgow, Lancaster, Leeds and UCLan which holds two conferences a year. London Mathematical Society Conference Grant – Scheme 3 – Joint Research Groups. Grant ref. 32328. October 2023. Value: £1200.
- London Mathematical Society Conference Grant – Scheme 9 – Celebrating New Appointments.
- Grant ref. 42218. July 2023. Value: £709 (inc. £210 contributed by the Jeremiah Horrocks Institute).
- Conference since 2023: ICRA, 21, Shanghai, August 2024
- CLAN, University of Central Lancashire, June 2024
- CLAN, University of Glasgow, February 2024
- Cluster Structures in the North, June 2023, University of Central Lancashire
Telephone:+44 (0)1772 893544
Email: Email:Dr Jonathan Wilson
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