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Dr Mathew Pugh
SFHEA
- Siarad Cymraeg
Timau a rolau for Mathew Pugh
Uwch Ddarlithydd
Trosolwyg
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 o fewn yr Ysgol, Coleg a Phrifysgol
- Cyfarwyddwr Dysgu ac Addysgu, Ysgol Mathemateg
- Cadeirydd, Bwrdd Astudiaethau Is-raddedig ac Ol-raddedig
- Aelod, Bwrdd Rheoli'r Ysgol
- Aelod, Panel Amgylchiadau Esgusodol yr Ysgol
- Aelod, Panel Myfyriwr-Staff Is-raddedig ac Ol-raddedig yr Ysgol
- Aelod, Panel Myfyriwr-Staff Myfyrwyr Ymchwil yr Ysgol
- Aelod, Gwrp Gweithredol y Gymraeg y Brifysgol
- Aelod, Is-Bwyllgor Cymeradwyo ac Ail-ddilysu Rhaglen y Brifysgol
Dyletswyddau allanol
- Aelod Panel Gwyddorau y Coleg Cymraeg Cenedlaethol
- Cyd-arweinydd Cystadleuaeth Mathemateg Seren
Cyhoeddiad
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)
Ymchwil
Mathematics Research
Mae fy ymchwil mathemateg wedi bod 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.
Yn fwy ddiweddar mae fy ymchwil wedi bod 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).
Ymcwhil Addysg Mathemateg
Mae gennyf ddiddordeb mewn addysg mathemateg ers meitin. Yn fwy ddiweddar mae fy niddordebau wedi crisialu o gwmpas y syniad o ymrwymiad myfyrwyr, yn benodol ymrwymiad academaidd myfyrwyr gyda'u hastudiaethau mathemateg mewn Addysg Uwch.
Mae yna ambell agwedd perthnasol i'r thema yma:
- Agweddau at addysgu, yn arbennig gyda garfannau mawr
- Annog ymrwymiad, yn arbennig trwy defnyddio asesiad
- Asesiad ac Adborth, yn fwy cyffredinol, i gefnogi dysgu ac ymrwymiad
- Cymunedau Dysgu
Cynadleddau a seminarau y trefnwyd
- CETL-MSOR 2023, Caerdydd, 7-8 Medi 2023 (gyda Jon Gillard, Rob Wilson)
- Workshop on Operator Algebras: Subfactors, K-theory, Conformal Field Theory, Gregynog, 27 Gorffennaf - 2 Awst 2022 (gyda Masaki Izumi, Gandalf Lechner, Ulrich Pennig)
- Cynhadledd Psychology of Mathematics Education 2022, arlein, 12 Gorffennaf 2022 (gyda Claire Ketnor, Dave Darwent)
- IMA HE Teaching & Learning Workshop: Educational Enquiry in the Mathematical Sciences, Bryste, 27 Mehefin 2022 (gyda Rob Wilson, Jos Gunns)
- Cydlynnydd seminar arlein clwstwr ymchwil Psychology of Mathematics Education, 2020-2024
- IMA HE Teaching & Learning Workshop: Feedback in Mathematics, Cardiff, 11 Mehefin 2019 (gyda Rob Wilson)
- LMS South Wales & South West Regional Meeting a Workshop on Algebraic Structures and Quantum Physics, Caerdydd, 13–15 Rhagfyr 2017 (gyda Gandalf Lechner, Simon Wood)
- LMS-WIMCS Workshop on Cluster Algebras and Preprojective Algebras, Caerdydd, 17–18 Hydref 2014
- INI-WIMCS Meeting on Noncommutative Geometry, Caerdydd, 16–20 Ebrill 2012 (gyda David Evans, Otgonbayar Uuye)
- WIMCS Workshop on Higher Gauge Theory, TQFT's and Categorification, Caerdydd, 9–10 Mai 2011 (gyda David Evans, Tim Porter)
- EU-NCG Focused Semester on Mathematical Physics, Caerdydd, Chwefror – Mehefin 2010 (gyda David Evans).
Addysgu
Yn bresennol rwyf yn addysgu cwrs Blwyddyn 3 ar Theori Clymau.
Yn y gorffennol rwyf wedi addysgu cyrsiau Blwyddyn 1 Calcwlws a Seiliau Mathemateg, a chwrs Blwyddyn 3 ar gyflwyniad i addysgu mathemateg mewn ysgol uwchradd.
Rwyf hefyd yn cefnogi darpariaeth cyfrwng Cymraeg yr Ysgol, gan gynnwys darparu diwtorialau ym Mlynyddoedd 1 a 2.
Bywgraffiad
Addysg a chymhwysterau
- 2009: PhD (Mathemateg), Prifysgol Caerdydd
- 2004: BSc Mathemateg, Prifysgol Caerdydd
Safleoedd academaidd blaenorol
- 2011 - presennol: Ysgol Mathemateg, Prifysgol Caerdydd
- 2008 - 2011: Cymrawd ymchwil, Prifysgol Caerdydd
Pwyllgorau ac adolygu
- 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, Ystafell Ystafell 3.20, Ffordd Senghennydd, Cathays, Caerdydd, CF24 4AG