Ewch i’r prif gynnwys
Dr Mathew Pugh

Dr Mathew Pugh

Uwch-ddarlithydd

Yr Ysgol Mathemateg

Email:
pughmj@cardiff.ac.uk
Telephone:
+44 (0)29 2087 6862
Location:
M/2.48, 2il lawr, Sefydliad Mathemateg, Heol Senghennydd, Caerdydd, CF24 4AG
Siarad Cymraeg

Mae gennyf ddiddordebau mewn algebrâu gweithredyddion, geometreg anghymudol a ffiseg fathemategol. Mae fy ngwaith wedi canolbwyntio ar y theori o ffwythiannau dosraniad sefydlog modiwlaidd ar gyfer modelau mecaneg ystadegol yn gysylltiedig â grwpiau Lie ac adeiladweithiau cysylltiedig o is-ffactorau pleth neu gategorïau tensor modiwlaidd a’u categorïau modiwl.

Yn benodol, rwyf wedi astudio amryw sefydlynnau sy’n gysylltiedig â’r is-ffactorau pleth yma, gan gynnwys systemau cell ar gyfer graffiau cynrychioliad, dosbarthiad o gategorïau modiwl, strwythurau algebra planar, mesurau sbectrol, ac algebrâu Jacobi a’u sefydlynnau homolegol.

Dyletswyddau gweinyddol

  • Arweinydd Asesiad ac Adborth
  • Dirprwy Reolwr Dysgu ac Addysgu
  • Cydlynydd darpariaeth cyfrwng Cymraeg

Grwp ymchwil

Geometreg, Algebra, Ffiseg Fathemategol a Topoleg

Addysg a chymhwysterau

  • 2009: PhD (Mathemateg), Prifysgol Caerdydd
  • 2004: BSc Mathemateg, Prifysgol Caerdydd

Trosolwg gyrfa

  • 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

2018

2016

2015

2013

2012

2011

2010

2009

Israddedig

Rwy'n dysgu ar y modiwlau canlynol:

  • MA1056 Seiliau Mathemateg II
  • MA3900 Cyflwyniad i Addysgu Mathemateg mewn Ysgol Uwchradd

Rwyf hefyd yn gyfrifol am darpariaeth cyfrwng Cymraeg ar draws y raglen israddedig.

Prosiectau BSc/MMath

  • 2018/19: Shauna Ford (prosiect MMath): Theori gynrychioliad o grwpiau feidraidd
  • 2018/19: Harry Smith (prosiect MMath): Theori gynrychioliad o grwpiau feidraidd

Prosiectau blaenorol

  • 2017/18: Heather Wadey (prosiect MMath): Theori gynrychioliad o grwpiau feidraidd
  • 2017/18: Mari Havard (prosiect BSc): Defnyddio cwestiynau sy'n asesu dealltwriaeth a chreadigrwydd mewn mathemateg
  • 2017/18: Jennifer Holden (prosiect BSc): A allem ni gynyddu effeithlonrwydd darparu adborth ar waith cartref heb effeithio'r ansawdd?
  • 2017/18: Lucy Hamilton (prosiect BSc): Bathodynnau digidol mewn addysg uwch
  • 2016/17: Lauren Bird (prosiect MMath): Theori gynrychioliad o grwpiau feidraidd
  • 2016/17: Ruth Cresswell (prosiect BSc): Gweithgareddau estyn allan mathemateg ar gyfer ysgol gynradd [ar y cyd gyda Federica Dragoni]
  • 2015/16: Conor Hunt (prosiect BSc): Theori gynrychioliad o grwpiau feidraidd
  • 2015/16: Abigail Dowler (prosiect BSc): Hyder, ymrwymiad a chyrhaeddiad mewn mathemateg [ar y cyd gyda Rob Wilson]
  • 2014/15: Ben Jones (prosiect BSc): Theori gynrychioliad o grwpiau feidraidd
  • 2013/14: Ryan Jones (prosiect BSc): Theori gynrychioliad o grwpiau feidraidd

Ôl-raddedig

  • Lorenzo Di Biase (ail oruchwyliwr, prif oruchwyliwr Timothy Logvinenko) PhD (Geometreg Algebraidd)

Wedi graddio

  • Stephen Moore (ail oruchwyliwr, prif oruchwyliwr David Evans) PhD: Non-Semisimple Planar Algebras
  • Claire Shelly (ail oruchwyliwr, prif oruchwyliwr David Evans) PhD 2013: Type III subfactors and planar algebras

My work has revolved around the theory of modular invariant partition functions for integrable statistical mechanical models associated to (rank two) Lie groups and related constructions of braided subfactors or modular tensor categories. The theory of alpha induction associates a modular invariant to a braided subfactor. Most of my research has 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.

In particular I have studied various invariants associated with these SU(3) braided subfactors. This included the computation of Ocneanu cells for the representation graphs which label the modular invariants, which we call the SU(3) ADE graphs. This led to the realisation of the SU(3) modular invariants by braided subfactors. Another direction was the formulation of A2-planar algebras which captured the structure contained in the subfactor double complex associated to the SU(3) ADE graphs and a description of certain modules over these A2-planar algebras. I have studied spectral measures for the SU(3) ADE graphs. In another direction I have constructed the Jacobi algebras, or almost Calabi-Yau algebras, associated to these SU(3) ADE graphs, and determined certain homological invariants of these algebras.

More recently I have sought to investigate similar invariants associated to braided subfactors for other rank two Lie groups, namely Sp(2), SO(5) and G2.

My ArXiv Articles

Conferences organised

Proffiliau allanol