![Mathew Pugh SFHEA](https://profiles-cardiff.imgix.net/attachments/206?w=200&h=200&auto=format&crop=faces&fit=crop&q=90")
Overview
Mae fy niddordebau mathemateg mewn algebrâu gweithredyddion - yn arbennig, theory is-ffactorau, y dechreuwyd gan fedalydd Fields, Vaughan Jones. Mae is-ffactorau yn gyffredinoliaeth o grwpiau sy’n cynnwys dimensiynau sydd ddim yn gyfanrifau. Maent yn amgodio cymesureddau cwantwm tu hwnt i grwpiau ac mae ganddyn nhw gymwysiadau yn Theori Maes Cydffurfiol (Conformal Field Theory, CFT). Rwyf wedi ehangu’r theory o is-ffactorau trwy luniadau perthnasol i grwpiau Lie. Mae fy ngwaith wedi darparu enghreifftiau newydd ar gyfer algebryddion, a oedd yn rhan o raglen 6-mis yn Sefydliad Isaac Newton, Caergrawnt, yn 2017.
Mae fy ymchwil presennol yn canolbwyntio ar ddosbarthu categorïau modiwl ar gyfer categorïau tensor modwlar sy’n ymddangos o fewn CFT, yn arbennig y rhai sy’n gysylltiedig i grwpiau Lie cryno, ond nid yn angenrheidiol yn gysylltiedig. Dechreuodd hyn gyda’r achos o SU(3) fel rhan o fy PhD, ond mae wedi ymestyn ers hynny i G2, Sp(2) ac SO(3).
Mae hefyd gennyf ddiddordebau mewn ymchwil addysg mathemateg, lle mae fy niddordebau yn bennaf yn ymwneud ag ymrwymiad myfyrwyr gyda'u astudiaethau. Mae agweddau arbennig o hyn yn cynnyws: agweddau ac ymarferion addysgu effeithiol, yn arbennig ar gyfer garfannau mawr; cymhellu ymrwymiad, yn arbennig trwy defnyddio asesiadau; a chyfeiriad meddwl ac agweddau at addysgu myfyrwyr.
Dyletswyddau gweinyddol
- Cyfarwyddwr Dysgu ac Addysgu
- Cydlynydd Darpariaeth Cyfrwng Cymraeg
Grwpiau ymchwil
Publication
2025
- Shaker, A., Brignell, C. and Pugh, M. 2025. The effect of incentivising pre-class reading on engagement and student performance. International Journal of Mathematical Education in Science and Technology 56(2), pp. 258-274. (10.1080/0020739X.2023.2214562)
2024
- Evans, D. and Pugh, M. 2024. Spectral measures for Sp(2). Pure and Applied Mathematics Quarterly 5, pp. 2249-2305. (10.4310/PAMQ.2023.v19.n5.a1)
2021
- Evans, D. E. and Pugh, M. 2021. Classification of module categories for SO(3)_{2m}. Advances in Mathematics 384, article number: 107713. (10.1016/j.aim.2021.107713)
2020
- Evans, D. E. and Pugh, M. J. 2020. Spectral measures for G2 II: finite subgroups. Reviews in Mathematical Physics 32(8), article number: 2050026. (10.1142/S0129055X20500269)
2019
- Ford, S., Gillard, J. and Pugh, M. 2019. Creating a taxonomy of mathematical errors for undergraduate mathematics. MSOR Connections 18(1), pp. 37-45. (10.21100/msor.v18i1)
2016
- Evans, D. E. and Pugh, M. . 2016. Spectral measures associated to rank two Lie groups and finite subgroups of GL(2,Z). Communications in Mathematical Physics 343, pp. 811-850. (10.1007/s00220-015-2434-5)
2015
- Evans, D. E. and Pugh, M. 2015. Spectral measures for G2. Communications in Mathematical Physics 337, pp. 1161-1197. (10.1007/s00220-015-2293-0)
- Evans, D. E. and Pugh, M. 2015. Spectral measures for Sp(2). [Online]. arXiv. Available at: http://arxiv.org/abs/1404.1912
2013
- Evans, D. E. and Pugh, M. J. 2013. Braided subfactors, spectral measures, planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants. Presented at: EU - NCG 4: EU - NCG 4th Annual Meeting, Bucharest, Romania, 25-30 April 2011 Presented at Popescu, I. and Purice, R. eds.Progress in Operator Algebras, Noncommutative Geometry, and their Applications: Proceedings of the 4th Annual Meeting of the European Noncommutative Geometry Network. pp. 17-60.
2012
- Evans, D. E. and Pugh, M. J. 2012. The Nakayama Automorphism of the almost Calabi-Yau Algebras associated to SU(3) modular invariants. Communications in Mathematical Physics 312(1), pp. 179-222. (10.1007/s00220-011-1389-4)
- Evans, D. E. and Pugh, M. J. 2012. On the homology of almost Calabi-Yau algebras associated to su(3) modular invariants. Journal of Algebra 368, pp. 92-125. (10.1016/j.jalgebra.2012.06.011)
2011
- Evans, D. E. and Pugh, M. J. 2011. A(2)-planar algebras II: Planar modules. Journal of Functional Analysis 261(7), pp. 1923-1954. (10.1016/j.jfa.2011.05.023)
- Evans, D. E. and Pugh, M. J. 2011. Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3). Communications in Mathematical Physics 301(3), pp. 771-809. (10.1007/s00220-010-1157-x)
2010
- Evans, D. E. and Pugh, M. J. 2010. Spectral measures and generating series for Nimrep graphs in subfactor theory. Communications in Mathematical Physics 295(2), pp. 363-413. (10.1007/s00220-009-0902-5)
- Evans, D. E. and Pugh, M. J. 2010. A2-planar algebras I. Quantum Topology 1(4), pp. 321-377. (10.4171/QT/8)
2009
- Evans, D. E. and Pugh, M. J. 2009. SU(3)-Goodman-De La Harpe-Jones Subfactors and the Realization of SU(3) Modular Invariants. Reviews in Mathematical Physics 21(7), pp. 877-928. (10.1142/S0129055X09003761)
- Evans, D. E. and Pugh, M. J. 2009. Ocneanu cells and Boltzmann weights for the SU(3) ADE graphs. Munster Journal of Mathematics 2, pp. 94-142.
2008
- Pugh, M. J. 2008. The Ising model and beyond. PhD Thesis, Cardiff University.
Articles
- Shaker, A., Brignell, C. and Pugh, M. 2025. The effect of incentivising pre-class reading on engagement and student performance. International Journal of Mathematical Education in Science and Technology 56(2), pp. 258-274. (10.1080/0020739X.2023.2214562)
- Evans, D. and Pugh, M. 2024. Spectral measures for Sp(2). Pure and Applied Mathematics Quarterly 5, pp. 2249-2305. (10.4310/PAMQ.2023.v19.n5.a1)
- Evans, D. E. and Pugh, M. 2021. Classification of module categories for SO(3)_{2m}. Advances in Mathematics 384, article number: 107713. (10.1016/j.aim.2021.107713)
- Evans, D. E. and Pugh, M. J. 2020. Spectral measures for G2 II: finite subgroups. Reviews in Mathematical Physics 32(8), article number: 2050026. (10.1142/S0129055X20500269)
- Ford, S., Gillard, J. and Pugh, M. 2019. Creating a taxonomy of mathematical errors for undergraduate mathematics. MSOR Connections 18(1), pp. 37-45. (10.21100/msor.v18i1)
- Evans, D. E. and Pugh, M. . 2016. Spectral measures associated to rank two Lie groups and finite subgroups of GL(2,Z). Communications in Mathematical Physics 343, pp. 811-850. (10.1007/s00220-015-2434-5)
- Evans, D. E. and Pugh, M. 2015. Spectral measures for G2. Communications in Mathematical Physics 337, pp. 1161-1197. (10.1007/s00220-015-2293-0)
- Evans, D. E. and Pugh, M. J. 2012. The Nakayama Automorphism of the almost Calabi-Yau Algebras associated to SU(3) modular invariants. Communications in Mathematical Physics 312(1), pp. 179-222. (10.1007/s00220-011-1389-4)
- Evans, D. E. and Pugh, M. J. 2012. On the homology of almost Calabi-Yau algebras associated to su(3) modular invariants. Journal of Algebra 368, pp. 92-125. (10.1016/j.jalgebra.2012.06.011)
- Evans, D. E. and Pugh, M. J. 2011. A(2)-planar algebras II: Planar modules. Journal of Functional Analysis 261(7), pp. 1923-1954. (10.1016/j.jfa.2011.05.023)
- Evans, D. E. and Pugh, M. J. 2011. Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3). Communications in Mathematical Physics 301(3), pp. 771-809. (10.1007/s00220-010-1157-x)
- Evans, D. E. and Pugh, M. J. 2010. Spectral measures and generating series for Nimrep graphs in subfactor theory. Communications in Mathematical Physics 295(2), pp. 363-413. (10.1007/s00220-009-0902-5)
- Evans, D. E. and Pugh, M. J. 2010. A2-planar algebras I. Quantum Topology 1(4), pp. 321-377. (10.4171/QT/8)
- Evans, D. E. and Pugh, M. J. 2009. SU(3)-Goodman-De La Harpe-Jones Subfactors and the Realization of SU(3) Modular Invariants. Reviews in Mathematical Physics 21(7), pp. 877-928. (10.1142/S0129055X09003761)
- Evans, D. E. and Pugh, M. J. 2009. Ocneanu cells and Boltzmann weights for the SU(3) ADE graphs. Munster Journal of Mathematics 2, pp. 94-142.
Conferences
- Evans, D. E. and Pugh, M. J. 2013. Braided subfactors, spectral measures, planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants. Presented at: EU - NCG 4: EU - NCG 4th Annual Meeting, Bucharest, Romania, 25-30 April 2011 Presented at Popescu, I. and Purice, R. eds.Progress in Operator Algebras, Noncommutative Geometry, and their Applications: Proceedings of the 4th Annual Meeting of the European Noncommutative Geometry Network. pp. 17-60.
Thesis
- Pugh, M. J. 2008. The Ising model and beyond. PhD Thesis, Cardiff University.
Websites
- Evans, D. E. and Pugh, M. 2015. Spectral measures for Sp(2). [Online]. arXiv. Available at: http://arxiv.org/abs/1404.1912
- Evans, D. E. and Pugh, M. J. 2012. The Nakayama Automorphism of the almost Calabi-Yau Algebras associated to SU(3) modular invariants. Communications in Mathematical Physics 312(1), pp. 179-222. (10.1007/s00220-011-1389-4)
- Evans, D. E. and Pugh, M. J. 2012. On the homology of almost Calabi-Yau algebras associated to su(3) modular invariants. Journal of Algebra 368, pp. 92-125. (10.1016/j.jalgebra.2012.06.011)
- Evans, D. E. and Pugh, M. J. 2010. Spectral measures and generating series for Nimrep graphs in subfactor theory. Communications in Mathematical Physics 295(2), pp. 363-413. (10.1007/s00220-009-0902-5)
- Evans, D. E. and Pugh, M. J. 2009. SU(3)-Goodman-De La Harpe-Jones Subfactors and the Realization of SU(3) Modular Invariants. Reviews in Mathematical Physics 21(7), pp. 877-928. (10.1142/S0129055X09003761)
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.
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 organised
- 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
Israddedig
Rwy'n dysgu ar y modiwlau canlynol:
- MA1056 Seiliau Mathemateg II
- MA3952 Modiwl Darllen (Theori Clymau)
- MA3900 Cyflwyniad i Addysgu Mathemateg mewn Ysgol Uwchradd
Rwyf hefyd yn gyfrifol am darpariaeth cyfrwng Cymraeg ar draws y raglen israddedig.
Prosiectau BSc/MMath
- 2020/21: Rhys Davies (prosiect MMath): Theori gynrychioliad o grwpiau feidraidd
Prosiectau blaenorol
- 2019/20: Sioned Owen (prosiect MMath): Cynrychioliadau o grwpiau feidraidd
- 2019/20: Foteinit Kleanthous (prosiect BSc): Investigating learning communities in mathematics at Cardiff University [ar y cyd gyda Rob Wilson]
- 2019/20: Jonathan Owens (prosiect BSc): Attendance at University [ar y cyd gyda Rob Wilson]
- 2018/19: Shauna Ford (prosiect MMath): Representation theory of the braid group
- 2018/19: Harry Smith (prosiect MMath): Representation theory of finite groups
- 2017/18: Mari Havard (prosiect BSc): Using questions which assess understanding and creativity in mathematics
- 2017/18: Jennifer Holden (prosiect BSc): Can we increase the effectiveness of feedback provided on homework without affecting its quality?
- 2017/18: Lucy Hamilton (prosiect BSc): Digital badges in higher education
- 2016/17: Ruth Cresswell (prosiect BSc): Mathematics outreach activities for primary school [ar y cyd gyda Federica Dragoni]
- 2015/16: Abigail Dowler (prosiect BSc): Confidence, engagement and attainment in mathematics [ar y cyd gyda Rob Wilson]
Biography
Addysg a chymhwysterau
- 2009: PhD (Mathemateg), Prifysgol Caerdydd
- 2004: BSc Mathemateg, Prifysgol Caerdydd
Academic positions
- 2011 - presennol: Ysgol Mathemateg, Prifysgol Caerdydd
- 2008 - 2011: Cymrawd ymchwil, Prifysgol Caerdydd
Committees and reviewing
-
- 2015 - presennol: Aelod o Banel Myfyriwr/Staff yr Ysgol
- 2013 - presennol: Aelod o Bwyllgor Dysgu ac Addysgu
- 2013 - presennol: Aelod o Gangen Prifysgol Caerdydd y Coleg Cymraeg Cenedlaethol
- 2014 - 2016: Aelod o Fwrdd Golygu'r Wefan Mathemateg
- 2011 - 2012: Aelod o'r Panel Arolygu Modiwlau
Pwyllgorau allanol
- 2011 - presennol: Aelod o Banel Pwnc Mathemateg a Ffiseg y Coleg Cymraeg Cenedlaethol
Contact Details
+44 29208 76862
Abacws, Room Room 3.20, Senghennydd Road, Cathays, Cardiff, CF24 4AG