![Matthew Lettington](https://profiles-cardiff.imgix.net/attachments/189?w=200&h=200&auto=format&crop=faces&fit=crop&q=90")
Dr Matthew Lettington
Uwch Ddarlithydd
Cyfarwyddwr Derbyn
- LettingtonMC@caerdydd.ac.uk
- +44 29208 75670
- Abacws, Ystafell 2.17, Ffordd Senghennydd, Cathays, Caerdydd, CF24 4AG
- Sylwebydd y cyfryngau
- Ar gael fel goruchwyliwr ôl-raddedig
Trosolwyg
Following the award of my PhD (Number Theory) in 2010, I joined Cardiff University as a Lecturer, obtaining a tenured position as an SBP Fellow in May 2012.
Administrative duties
Undergraduate Project Co-Ordinator
School of Mathematics Newsletter Editor
Cyhoeddiad
2023
- Hindmarsh, J. L. and Lettington, M. C. 2023. On polynomial transformations preserving purely imaginary zeros. Integral Transforms and Special Functions 34(7), pp. 522-536. (10.1080/10652469.2022.2155643)
- Lettington, M. and Schmidt, K. 2023. On the sum of left and right circulant matrices. Linear Algebra and its Applications 658, pp. 62-85. (10.1016/j.laa.2022.10.024)
2022
- Higham, N. J. and Lettington, M. C. 2022. Optimizing and factorizing the Wilson matrix. American Mathematical Monthly 129(5), pp. 454-465. (10.1080/00029890.2022.2038006)
2021
- Higham, N. J., Lettington, M. C. and Schmidt, K. M. 2021. Integer matrix factorisations, superalgebras and the quadratic form obstruction. Linear Algebra and its Applications 622, pp. 250-267. (10.1016/j.laa.2021.03.028)
2020
- Lettington, M. C. and Schmidt, K. M. 2020. Divisor functions and the number of sum systems. Integers 20, article number: A61.
- Hill, S. L., Huxley, M. N., Lettington, M. C. and Schmidt, K. M. 2020. Some properties and applications of non-trivial divisor functions. Ramanujan Journal 51 (10.1007/s11139-018-0093-9)
- Coffey, M. W. and Lettington, M. C. 2020. Binomial polynomials mimicking Riemann's zeta function. Integral Transforms and Special Functions 31(11), pp. 856-872. (10.1080/10652469.2020.1755672)
2019
- Huxley, M. N., Lettington, M. C. and Schmidt, K. M. 2019. On the structure of additive systems of integers. Periodica Mathematica Hungarica 78, pp. 178-199. (10.1007/s10998-018-00275-w)
2018
- Hill, S., Lettington, M. C. and Schmidt, K. M. 2018. Block representations and spectral properties of constant sum matrices. Electronic Journal of Linear Algebra 34, pp. 170-190. (10.13001/1081-3810.3530)
2017
- Lettington, M. C., Schmidt, K. M. and Hill, S. 2017. On superalgebras of matrices with symmetry properties. Linear and Multilinear Algebra 66(8), pp. 1538-1563. (10.1080/03081087.2017.1363153)
- Coffey, M. W., Hindmarsh, J. L., Lettington, M. C. and Pryce, J. D. 2017. On higher-dimensional Fibonacci numbers, Chebyshev polynomials and sequences of vector convergents. Journal de Theorie des Nombres de Bordeaux 29(2), pp. 369-423. (10.5802/jtnb.985)
- Coffey, M. W. and Lettington, M. C. 2017. Binomial polynomials mimicking Riemann's Zeta Function. [Online]. arXiv. Available at: https://arxiv.org/abs/1703.09251
2016
- Lettington, M. and Coffey, M. W. 2016. On Fibonacci polynomial expressions for sums of m-th powers, their implications for Faulhaber's formula and some theorems of fermat. [Online]. arXiv. Available at: https://arxiv.org/abs/1510.05402
2015
- Coffey, M. W. and Lettington, M. C. 2015. Mellin transforms with only critical zeros: Legendre functions. Journal of Number Theory 148, pp. 507-536. (10.1016/j.jnt.2014.07.021)
2014
- Brunnock, R., Lettington, M. C. and Schmidt, K. M. 2014. On square roots and norms of matrices with symmetry properties. Linear Algebra and its Applications 459, pp. 175-207. (10.1016/j.laa.2014.06.054)
2013
- Lettington, M. C. 2013. A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function. Acta Arithmetica 158(1), pp. 1-31. (10.4064/aa158-1-1)
2011
- Lettington, M. C. 2011. Fleck's congruence, associated magic squares and a zeta identity. Functiones et Approximatio, Commentarii Mathematici 45(2), pp. 165-205. (10.7169/facm/1323705813)
2010
- Lettington, M. C. 2010. Integer points close to convex hypersurfaces. Acta Arithmetica 141(1), pp. 73-101. (10.4064/aa141-1-4)
2009
- Lettington, M. C. 2009. Integer points close to convex surfaces. Acta Arithmetica 138(1), pp. 1-23. (10.4064/aa138-1-1)
2008
- Lettington, M. C. 2008. Topics related to the theory of numbers: integer points close to convex hypersurfaces, associated magic squares and a zeta identity. PhD Thesis, Cardiff University.
Erthyglau
- Hindmarsh, J. L. and Lettington, M. C. 2023. On polynomial transformations preserving purely imaginary zeros. Integral Transforms and Special Functions 34(7), pp. 522-536. (10.1080/10652469.2022.2155643)
- Lettington, M. and Schmidt, K. 2023. On the sum of left and right circulant matrices. Linear Algebra and its Applications 658, pp. 62-85. (10.1016/j.laa.2022.10.024)
- Higham, N. J. and Lettington, M. C. 2022. Optimizing and factorizing the Wilson matrix. American Mathematical Monthly 129(5), pp. 454-465. (10.1080/00029890.2022.2038006)
- Higham, N. J., Lettington, M. C. and Schmidt, K. M. 2021. Integer matrix factorisations, superalgebras and the quadratic form obstruction. Linear Algebra and its Applications 622, pp. 250-267. (10.1016/j.laa.2021.03.028)
- Lettington, M. C. and Schmidt, K. M. 2020. Divisor functions and the number of sum systems. Integers 20, article number: A61.
- Hill, S. L., Huxley, M. N., Lettington, M. C. and Schmidt, K. M. 2020. Some properties and applications of non-trivial divisor functions. Ramanujan Journal 51 (10.1007/s11139-018-0093-9)
- Coffey, M. W. and Lettington, M. C. 2020. Binomial polynomials mimicking Riemann's zeta function. Integral Transforms and Special Functions 31(11), pp. 856-872. (10.1080/10652469.2020.1755672)
- Huxley, M. N., Lettington, M. C. and Schmidt, K. M. 2019. On the structure of additive systems of integers. Periodica Mathematica Hungarica 78, pp. 178-199. (10.1007/s10998-018-00275-w)
- Hill, S., Lettington, M. C. and Schmidt, K. M. 2018. Block representations and spectral properties of constant sum matrices. Electronic Journal of Linear Algebra 34, pp. 170-190. (10.13001/1081-3810.3530)
- Lettington, M. C., Schmidt, K. M. and Hill, S. 2017. On superalgebras of matrices with symmetry properties. Linear and Multilinear Algebra 66(8), pp. 1538-1563. (10.1080/03081087.2017.1363153)
- Coffey, M. W., Hindmarsh, J. L., Lettington, M. C. and Pryce, J. D. 2017. On higher-dimensional Fibonacci numbers, Chebyshev polynomials and sequences of vector convergents. Journal de Theorie des Nombres de Bordeaux 29(2), pp. 369-423. (10.5802/jtnb.985)
- Coffey, M. W. and Lettington, M. C. 2015. Mellin transforms with only critical zeros: Legendre functions. Journal of Number Theory 148, pp. 507-536. (10.1016/j.jnt.2014.07.021)
- Brunnock, R., Lettington, M. C. and Schmidt, K. M. 2014. On square roots and norms of matrices with symmetry properties. Linear Algebra and its Applications 459, pp. 175-207. (10.1016/j.laa.2014.06.054)
- Lettington, M. C. 2013. A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function. Acta Arithmetica 158(1), pp. 1-31. (10.4064/aa158-1-1)
- Lettington, M. C. 2011. Fleck's congruence, associated magic squares and a zeta identity. Functiones et Approximatio, Commentarii Mathematici 45(2), pp. 165-205. (10.7169/facm/1323705813)
- Lettington, M. C. 2010. Integer points close to convex hypersurfaces. Acta Arithmetica 141(1), pp. 73-101. (10.4064/aa141-1-4)
- Lettington, M. C. 2009. Integer points close to convex surfaces. Acta Arithmetica 138(1), pp. 1-23. (10.4064/aa138-1-1)
Gosodiad
- Lettington, M. C. 2008. Topics related to the theory of numbers: integer points close to convex hypersurfaces, associated magic squares and a zeta identity. PhD Thesis, Cardiff University.
Gwefannau
- Coffey, M. W. and Lettington, M. C. 2017. Binomial polynomials mimicking Riemann's Zeta Function. [Online]. arXiv. Available at: https://arxiv.org/abs/1703.09251
- Lettington, M. and Coffey, M. W. 2016. On Fibonacci polynomial expressions for sums of m-th powers, their implications for Faulhaber's formula and some theorems of fermat. [Online]. arXiv. Available at: https://arxiv.org/abs/1510.05402
- Hindmarsh, J. L. and Lettington, M. C. 2023. On polynomial transformations preserving purely imaginary zeros. Integral Transforms and Special Functions 34(7), pp. 522-536. (10.1080/10652469.2022.2155643)
- Lettington, M. and Schmidt, K. 2023. On the sum of left and right circulant matrices. Linear Algebra and its Applications 658, pp. 62-85. (10.1016/j.laa.2022.10.024)
- Higham, N. J. and Lettington, M. C. 2022. Optimizing and factorizing the Wilson matrix. American Mathematical Monthly 129(5), pp. 454-465. (10.1080/00029890.2022.2038006)
- Higham, N. J., Lettington, M. C. and Schmidt, K. M. 2021. Integer matrix factorisations, superalgebras and the quadratic form obstruction. Linear Algebra and its Applications 622, pp. 250-267. (10.1016/j.laa.2021.03.028)
- Lettington, M. C. and Schmidt, K. M. 2020. Divisor functions and the number of sum systems. Integers 20, article number: A61.
- Hill, S. L., Huxley, M. N., Lettington, M. C. and Schmidt, K. M. 2020. Some properties and applications of non-trivial divisor functions. Ramanujan Journal 51 (10.1007/s11139-018-0093-9)
- Coffey, M. W. and Lettington, M. C. 2020. Binomial polynomials mimicking Riemann's zeta function. Integral Transforms and Special Functions 31(11), pp. 856-872. (10.1080/10652469.2020.1755672)
- Huxley, M. N., Lettington, M. C. and Schmidt, K. M. 2019. On the structure of additive systems of integers. Periodica Mathematica Hungarica 78, pp. 178-199. (10.1007/s10998-018-00275-w)
- Hill, S., Lettington, M. C. and Schmidt, K. M. 2018. Block representations and spectral properties of constant sum matrices. Electronic Journal of Linear Algebra 34, pp. 170-190. (10.13001/1081-3810.3530)
- Lettington, M. C., Schmidt, K. M. and Hill, S. 2017. On superalgebras of matrices with symmetry properties. Linear and Multilinear Algebra 66(8), pp. 1538-1563. (10.1080/03081087.2017.1363153)
- Coffey, M. W., Hindmarsh, J. L., Lettington, M. C. and Pryce, J. D. 2017. On higher-dimensional Fibonacci numbers, Chebyshev polynomials and sequences of vector convergents. Journal de Theorie des Nombres de Bordeaux 29(2), pp. 369-423. (10.5802/jtnb.985)
- Lettington, M. and Coffey, M. W. 2016. On Fibonacci polynomial expressions for sums of m-th powers, their implications for Faulhaber's formula and some theorems of fermat. [Online]. arXiv. Available at: https://arxiv.org/abs/1510.05402
- Coffey, M. W. and Lettington, M. C. 2015. Mellin transforms with only critical zeros: Legendre functions. Journal of Number Theory 148, pp. 507-536. (10.1016/j.jnt.2014.07.021)
- Brunnock, R., Lettington, M. C. and Schmidt, K. M. 2014. On square roots and norms of matrices with symmetry properties. Linear Algebra and its Applications 459, pp. 175-207. (10.1016/j.laa.2014.06.054)
- Lettington, M. C. 2013. A trio of Bernoulli relations, their implications for the Ramanujan polynomials and the special values of the Riemann zeta function. Acta Arithmetica 158(1), pp. 1-31. (10.4064/aa158-1-1)
- Lettington, M. C. 2011. Fleck's congruence, associated magic squares and a zeta identity. Functiones et Approximatio, Commentarii Mathematici 45(2), pp. 165-205. (10.7169/facm/1323705813)
- Lettington, M. C. 2010. Integer points close to convex hypersurfaces. Acta Arithmetica 141(1), pp. 73-101. (10.4064/aa141-1-4)
- Lettington, M. C. 2009. Integer points close to convex surfaces. Acta Arithmetica 138(1), pp. 1-23. (10.4064/aa138-1-1)
- Lettington, M. C. 2008. Topics related to the theory of numbers: integer points close to convex hypersurfaces, associated magic squares and a zeta identity. PhD Thesis, Cardiff University.
Ymchwil
Research interests:
- Integer points close to convex hypersurfaces and polytopes.
- Identities for the Zeta function at integer values.
- Combinatorial and number theoretic properties of symmetric matrices under matrix multiplication.
- Modelling techniques for industry (such as SSA).
Addysgu
- MA4011 Analytic Number Theory
- MA0216 Elementary Number Theory II
- MA3004 Combinatorics
Bywgraffiad
Anrhydeddau a dyfarniadau
SBP Fellowship awarded May 2012
Aelodaethau proffesiynol
Memeber of the London Mathematical Society (LMS)
Safleoedd academaidd blaenorol
- June 2006 - Aug 2010: Mathematical Consultant, JSC Management und-Technologieberatung AG, Eltville, Germany
- Oct. 2001 - April 2010: Lecturer in Mathematics, Gloucestershire College, Cheltenham.
Ymrwymiadau siarad cyhoeddus
- Awst 2008. Dull deinamig o ragweld gwerthu cynnyrch. SMiCR, Caerdydd.
-
Mawrth 2012. Cynnydd diweddar wrth ddosbarthu pwyntiau dellt ger arwynebau amgrwm a pholytopau. Rhaglen Seminarau Dadansoddi, Caerdydd.
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Mai 2013. Cynnydd diweddar mewn perthynas â Bernoulli, eu goblygiadau i'r polynomialau Ramanujan a gwerthoedd arbennig swyddogaeth zeta Riemann, Colocwiwm Mathemateg Cymru, Gregynog.
- Chwefror 2014. O ran cydgyfeiriannau rhesymegol i gosin lluosrifau rhesymegol Pi, Rhaglen Seminar Dadansoddi, Caerdydd.
- Mai 2014. Dilyniannau Lucas a Fibonacci Uwch-Ddimensiwn, Colocwiwm Mathemateg Cymru, Gregynog.
- Mawrth 2015, dilyniannau Fibonacci sy'n rhyngblethu dimensiwn uwch, ffracsiynau parhaus a polynomialau Chebyshev (haniaethol), LMS, WIMCS – Diwrnod Dadansoddi Caerfaddon, Prifysgol Abertawe.
- Gorffennaf 2015, ar ddilyniant Fibonacci sy'n rhyngblethu dimensiwn uwch, ffracsiynau parhaus a polynomialau Chebyshev (haniaethol), 29ain Journées Arithmétiques JA 2015, Prifysgol Debrecen, Hwngari.
- Dydd Gwener, Medi 4 2015, 3.00pm, Neuadd Chauvenet, Ystafell 143, Sgwrs wahoddedig, Mathemateg Gymhwysol ac Ystadegau Collocwiwm , Ysgol Mwyngloddiau Colorado, ar ddilyniant Fibonacci sy'n rhyngblethu dimensiwn uwch. (haniaethol).
- Mai 2016. Ar gynrychioliadau bloc ac eiddo sbectrol Matrices Sgwâr Semimagic, Colocwiwm Mathemateg Cymru, Gregynog.
- Hydref 14 2016, Modern Aspects of Analysis and Scientific Computing (A joint University Cardiff — Cyfarfod KU Leuven), Sgwrs Lawn o'r enw Ar fynegiannau polynomial ar gyfer dilyniannau Fibonacci uwch-ddimensiwn, symiau Faulhaber, a rhai theoremau Fermat.
- Ionawr 24, 2017, Cyfweliad teledu gyda BBC Wales Today a Chyfweliad Radio yn fyw ar Good Morning Wales ynghylch y stori arloesol a ddarlledwyd gan BBCs The One Show, ac ymddangos ar dudalen flaen papur newydd The Times, o'r enw "It Doesn't Add Up."
- Mawrth 21, 2017, Tinted Lens – Canolfan Gelfyddydau Chapter, Caerdydd, Sgwrs Invited o'r enw Mathemateg Concrit mewn perthynas â ffilm Theodore Melfi The Hidden Figures.
- Gorffennaf 3 2017, Ar Polynomialau Binomial Mimicking Riemann yn Zeta Swyddogaeth, 30th Journées Arithmétiques JA 2017, Prifysgol Caen, Ffrainc.
- Mai 2018. Ar systemau swm-a-pellter, matricsau sgwâr cildroadwy a swyddogaethau rhanyddol, Colocwiwm Mathemateg Cymru, Gregynog.
- Mehefin 2018. Ar systemau swm-a-pellter, matricsau sgwâr cildroadwy a swyddogaethau rhanyddol, matricsau a chymwysiadau Bohemaidd, Mehefin 20-22, 2018, Prifysgol Manceinion. http://www.maths.manchester.ac.uk/~higham/conferences/bohemian/slides_lettington.pdf
- Hydref 2018. Ar systemau swm-a-pellter, matricsau sgwâr cildroadwy a swyddogaethau rhanyddol, gwahodd Sgwrs Colloquium , Y Brifysgol Agored, Milton Keynes, y DU, http://mathematics.open.ac.uk/events/sum-and-distance-systems-reversible-square-matrices-and-divisor-functions
- Tachwedd 2018. Ar systemau swm-a-pellter, matricsau sgwâr cildroadwy a swyddogaethau rhanyddol, gwahodd seminar sgwrs, Prifysgol Essex, Colchester, UK, https://www.essex.ac.uk/events/2018/11/15/department-of-mathematical-sciences-seminar
- Gorffennaf 2019. Ar fatricsau sgwâr cildroadwy a swyddogaethau Divisor, gwahodd Minisymposiwm Sgwrs (MS A6-2-2 9) ar Matrices Bohemian, a drefnwyd gan Nick higham a Rob Corless, SIAM 2019, Valencia, Sbaen.
- Ionawr 2020, Sgwrs Collocwiwm Gwahoddedig, Prifysgol De Cymru, Swyddogaethau Rhannydd a Systemau Sum, https://maths.research.southwales.ac.uk/upcoming-seminars/matthew-lettington-combinatorics/
- Chwefror 2020, gwahodd Sgwrs Seminar Mathemateg Pur, Prifysgol Ddarllen, Swyddogaethau Rhannydd a nifer y Systemau Swm https://janivirtanen.wordpress.com/pure-mathematics-seminar-at-reading/
- Dydd Gwener 23 Gorffennaf 2021, gwahoddodd Bohemain Matrices Minisymposium sgwrs o'r enw Cynnydd Diweddar yn Ffactor Rhesymegol Mathemategwyr Cyfanrif, SIAM AN21, Spokane, Washington SIAM AN21 Minisymposiwm ar Fatricsau a Cheisiadau Bohemaidd – Nick Higham (nhigham.com) Gweler hefyd Rhaglen Gynadledda Ar-lein (siam.org)
- Dydd Mawrth 23 Mai 2022. Cyfrannodd Colocwiwm Mathemateg Cymru 2022, o'r enw Integer Matrix Factorisation a'r Rhwystr Ffurf Cwadratig, Neuadd Gregynog, Tregynon, Sir Drefaldwyn, Cymru.
- Dydd Mawrth 9 Mai 2023. Gwahoddodd Cyfres Collocwiwm y Brifysgol Agored o'r enw On Multi-factorisations, Sum Systems and Number Walls, The Open University, Milton Keynes, Buckinghamshire, UK.
- Dydd Mawrth 24 Mehefin 2023. Cyfrannodd Cynhadledd 25th ILAS, matricsau Bohemaidd a phynciau cysylltiedig mewn minisymposiwm theori matrics, o'r enw Ar ddadelfeniad orthogonal matricsau sgwâr go iawn
dros y dosbarthiadau cymesuredd cyd-Ladin a lled-hud. Gweler MSC26.pdf (ilas2023.es) - Dydd Llun 31 Hydref 2023. Cyfres Seminarau Algebra llinol Rhifiadol Prifysgol Manceinion, a wahoddwyd i siarad o'r enw On the co-Latin and semi-magic symmetry classes, Manchester University, UK.
ESGI 80 Cydweithio
Ebrill 2011. Llwytho ar y grid trydan o systemau storio ynni dosbarthedig.
Allgymorth addysgol a'r cyfryngau
- Yn 2015 cynghorais a chyfranogais mewn pennod ar gyfer y gyfres sianel Discovery o'r enw Man V Expert, yn cynnwys yr enwog Alexis Conran, a'r Oxford Number Theorist Professor Minhyong Kim.
- Ddiwedd 2016 lluniais dîm o fyfyrwyr PhD a staff o Ysgol Mathemateg Caerdydd i ymchwilio i wallau mewn Llyfr Mathemateg TGAU ar ran y BBC The One Show. Cafodd y canlyniadau eu dangos ar dudalen flaen papur newydd The Times ac fe'u darlledwyd ar y BBC The One Show ar Ionawr 24, 2017. Cafodd y stori ei chynnwys hefyd mewn nifer o bapurau newydd cenedlaethol eraill gan gynnwys The Herald, The Independent, The Daily Mirror a The Daily Express. Ar yr un diwrnod fe wnes i ymddangos ar y teledu (BBC Wales Today) a Radio (Good Morning Wales) i drafod ein canfyddiadau.
- Ym mis Rhagfyr 2018, ar y cyd ag Admiral a Brand Content, ysgrifennais y fathemateg sy'n sail i gyfrifiannell hynod lwyddiannus Admiral Bauble. Mae hyn yn gofyn am fanylion eich coeden Nadolig a'ch dewisiadau, y mae'n cyfrifo nifer y baubles a hyd y goleuadau teg sydd eu hangen. Mae Cyfrifiannell Bauble Admiral ar gael yma Cyfrifiannell Bauble - Admiral
- Ar ddydd Gwener 15 Tachwedd 2019 fe wnes i ymddangos ar Raglen Today Radio 4 yn fyw i ddarllen pos roeddwn i wedi'i chyfansoddi yn amgodio hanes Prifysgol Caerdydd yn arddull epigram Diophantus o Alexandria tua 300 OC. Mae'r pos yn darllen fel a ganlyn:
'Prifysgol Caerdydd', y rhyfeddod, wel,
Ym mis Tachwedd 2018, mae'r pos yn dweud pa mor hen:
Cychwynnodd y cyfnod cynnar am y naw mlynedd llawn,
Un rhan o nawfed bywyd yn ddiweddarach, mae adeilad yn ymddangos.
Ar ôl tair rhan o bump yn fwy, unais fy amod;
Ac un pymthegfed arall, pwerau llawn, a roddwyd.
Un mlynedd ar hugain yn ddiweddarach ac yr wyf yn awr yn hedfan yn uchel,
Wrth galon prifddinas Cymru, pa mor hen ydw i?
Gellir dod o hyd i'r ateb yn https://www.bbc.co.uk/programmes/articles/26hdyfBgB2PSWs3kMBp0kJ2/today-puzzle-612
Pwyllgorau ac adolygu
Year Three Tutor
Meysydd goruchwyliaeth
Project Descriptions
The general theme is centred on constructions and limits of sequences of vector convergents, systems of polynomials and generating function matrices, including the application of special function theory. There are a number of possible directions within this project as there are currently many areas that are of interest from description/categorisation theories to general unifying approaches and extensions of current methodologies
The student will learn about ideas from number theory and mathematical analysis. The project will involve an element of numerical analysis via Mathematica.
The student will learn about ideas from number theory and mathematical analysis. The project will involve an element of numerical analysis via Mathematica.
Goruchwyliaeth gyfredol
Grant Jones
Myfyriwr ymchwil
Prosiectau'r gorffennol
Myfyrwyr PhD llwyddiannus:
- 2017 Dilbak Mohammed (ail oruchwyliwr)
- Sally L. Hill (goruchwyliwr cyntaf) 2018
- 2021 David M. Humphreys (goruchwyliwr cyntaf)