Dr Mathew Pugh

SFHEA

Publication

• Date
• Type
• Promoted

Research

Mathematics Research

Most of my mathematics research has revolved around the theory of modular invariant partition functions for integrable statistical mechanical models associated to Lie groups and related constructions of braided subfactors or modular tensor categories. My early research focused on braided subfactors associated to the SU(3) modular invariants, although more recently I have focused on modular invariants for other rank two Lie groups, namely Sp(2), SO(5) and G₂, and also non-connected groups such as the rank one Lie group SO(3). This has led to the classification of module categories for the modular tensor categories associated with SU(3) and, more recently, SO(3).

In particular, I have studied various invariants associated with these braided subfactors. This includes the computation of cell systems for the representation graphs (also called nimreps) which label the modular invariants, and the realisation of modular invariants by braided subfactors. I have studied spectral measures for the nimrep graphs. And in another direction I have constructed the higher preprojective algebras or corresponding Jacobi algebras associated to these nimreps, including certain homological invariants of these algebras.

My ArXiv Articles

Mathematics Education Research

I have been interested in mathematics education for a long time. More recently my interests have converged and crystallised around the idea of student engagement, specifically students' academic engagement with their mathematics studies at HE.

There are many relevant facets to this overarching theme:

• Approaches to teaching, particularly in large cohorts
• Incentivising engagement, particularly through use of assessment
• Assessment and Feedback, more generally, in supporting learning and engagement
• Learning communities
• Students' mindsets and approaches to learning

Some particular research interests going forward:

• Which forms of engagement are most effective for learning mathematics?
• What factors influence student engagement in mathematics?
• How to improve student engagement most effectively for learning?
• Is incentivised engagement effective for learning?

Conferences & Seminars organised

• CETL-MSOR 2023, Cardiff, 7-8 September 2023 (with Jon Gillard, Rob Wilson)
• Workshop on Operator Algebras: Subfactors, K-theory, Conformal Field Theory, Gregynog Hall, 27 July - 2 August 2022 (with Masaki Izumi, Gandalf Lechner, Ulrich Pennig)
• Psychology of Mathematics Education conference 2022, online, 12 July 2022 (with Claire Ketnor, Dave Darwent)
• IMA HE Teaching & Learning Workshop on Educational Enquiry in the Mathematical Sciences, Bristol, 27 June 2022 (with Rob Wilson, Jos Gunns)
• Psychology of Mathematics Education research cluster online seminar organiser, 2020-2024
• IMA HE Teaching & Learning Workshop on Feedback in Mathematics, Cardiff, 11 June 2019 (with Rob Wilson)
• LMS South Wales & South West Regional Meeting and Workshop on Algebraic Structures and Quantum Physics, Cardiff, 13–15 December 2017 (with Gandalf Lechner, Simon Wood)
• LMS-WIMCS Workshop on Cluster Algebras and Preprojective Algebras, Cardiff, 17–18 October 2014
• INI-WIMCS Meeting on Noncommutative Geometry, Cardiff, 16–20 April 2012 (local organiser with David Evans, Otgonbayar Uuye)
• WIMCS Workshop on Higher Gauge Theory, TQFT's and Categorification, Cardiff, 9–10 May 2011 (with David Evans Tim Porter)
• EU-NCG Focused Semester on Mathematical Physics, Cardiff, February – June 2010 (with David Evans).

Teaching

I currently teach a Year 3 course on Knot Theory.

In the past I have also taught Year 1 Calculus and Foundations of Mathematics courses, and a Year 3 introduction to teaching mathematics in secondary schools.

I also support the School's Welsh-medium provision, including delivering tutorial classes in Welsh in Years 1 and 2.

Biography

Education & Qualifications

• 2020: Senior Fellow of the Higher Education Academy (SFHEA)
• 2013: Fellow of the Higher Education Academy (FHEA)
• 2009: PhD (Mathematics), Cardiff University
• 2004: BSc Mathematics, Cardiff University

Academic positions

• 2011 - present: School of Mathematics, Cardiff University
• 2008 - 2011: Research Associate, Cardiff University

Committees and reviewing

• • 2022 - present: School Education & Student Experience Committee chair
  • 2022 - present: School PGR Student-Staff Panel member
  • 2022 - present: University Programme Approval and Revalidation Sub-Committee member
  • 2021 - present: Mathematics UG & PGT Board of Studies chair
  • 2021 - present: School Extenuating Circumstances Panel member
  • 2017 - present: University Welsh Language Executive Group member
  • 2015 - present: School UG & PGT Student-Staff Panel member
  • 2013 - present: Coleg Cymraeg Cenedlaethol Cardiff University Branch member
  • 2013 - 2019: School Learning & Teaching Committee member
  • 2014 - 2016: School Website Review Board member
  • 2011 - 2012: School Module Review panel member

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• External Roles

  • 2025 - present: European Consortium for Mathematics in Industry (ECMI) Educational Committee member
  • 2024 - present: External examiner, University of Kent
  • 2022 - present: Seren Mathematics Competition co-lead
  • 2011 - present: Coleg Cymraeg Cenedlaethol Sciences Panel member