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Yr Athro Roger Behrend
Cadeirydd Personol
- BehrendR@caerdydd.ac.uk
- +44 29208 75543
- Abacws, Ystafell 3.70, Ffordd Senghennydd, Cathays, Caerdydd, CF24 4AG
Trosolwyg
Rolau cyfredol
- Pennaeth Geometreg, Algebra, Ffiseg Fathemategol a Grŵp Ymchwil Topoleg.
- Cydlynydd yr Ysgol Mathemateg Colloquia.
- Aelod o Senedd y Brifysgol.
- Tiwtor Blwyddyn 4 yr Ysgol Mathemateg.
Ymchwil cyfredol
- Combinatorics, gan gynnwys matricsau arwydd eiledol, graffiau, llwybrau dellt, parwydydd awyren a pholytopau.
Addysgu cyfredol
- MA1008 Algebra Llinol I
- MA2014 Algebra I: Grwpiau
Aelodaeth broffesiynol
- Cymdeithas Mathemategol America
- Sefydliad Ffiseg
- Cymdeithas Mathemategol Llundain
Cyhoeddiad
2024
- Behrend, R. E. 2024. Ehrhart polynomials of partial permutohedra. [Online]. arXiv. Available at: https://arxiv.org/abs/2403.06975
2023
- Behrend, R. E., Fischer, I. and Koutschan, C. 2023. Diagonally symmetric alternating sign matrices. [Online]. arXiv: arXiv. (10.48550/arXiv.2309.08446) Available at: https://arxiv.org/abs/2309.08446
- Behrend, R. E., Castillo, F., Chavez, A., Diaz-Lopez, A., Escobar, L., Harris, P. E. and Insko, E. 2023. Partial permutohedra. Presented at: 35th Conference on Formal Power Series and Algebraic Combinatorics, 17-21 July 2023, Vol. 89B.
- Behrend, R. E., Castillo, F., Chavez, A., Diaz-Lopez, A., Escobar, L., Harris, P. E. and Insko, E. 2023. Partial permutohedra. [Online]. arXiv: arXiv. (10.48550/arXiv.2207.14253) Available at: https://arxiv.org/abs/2207.14253
2020
- Ayyer, A., Behrend, R. E. and Fischer, I. 2020. Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order. Advances in Mathematics 367, article number: 107125. (10.1016/j.aim.2020.107125)
2019
- Ayyer, A. and Behrend, R. E. 2019. Factorization theorems for classical group characters, with applications to alternating sign matrices and plane partitions. Journal of Combinatorial Theory, Series A 165, pp. 78-105. (10.1016/j.jcta.2019.01.001)
2018
- Behrend, R. 2018. An update on matters discussed at Oberwolfach by Ian Macdonald in May 1977 and David Robbins in May 1982. Presented at: Oberwolfach Workshop 1820, Oberwolfach, 13 - 19 May 2018Enumerative Combinatorics, Vol. 15. Oberwolfach Reports Vol. 23. European Mathematical Society pp. 1416-1418., (10.4171/OWR/2018/23)
2017
- Behrend, R. E., Fischer, I. and Konvalinka, M. 2017. Diagonally and antidiagonally symmetric alternating sign matrices of odd order. Advances in Mathematics 315, pp. 324-365. (10.1016/j.aim.2017.05.014)
2016
- Behrend, R. E., Fischer, I. and Konvalinka, M. 2016. Diagonally and antidiagonally symmetric alternating sign matrices of odd order. Discrete Mathematics and Theoretical Computer Science BC, pp. 131-142.
2015
- Behrend, R. E., O, S. and West, D. B. 2015. Sharp lower bounds on the fractional matching number. Discrete Applied Mathematics 186, pp. 272-274. (10.1016/j.dam.2015.01.014)
2014
- Behrend, R. E. 2014. Alternating sign matrix enumeration involving numbers of inversions and -1's, and positions of boundary 1's. RIMS Kokyuroku 1913, pp. 1-21., article number: 1.
2013
- Behrend, R. E. 2013. Fractional perfect b-matching polytopes I: General theory. Linear Algebra and its Applications 439(12), pp. 3822-3858. (10.1016/j.laa.2013.10.001)
- Behrend, R. E. 2013. Multiply-refined enumeration of alternating sign matrices. Advances in Mathematics 245, pp. 439-499. (10.1016/j.aim.2013.05.026)
- Behrend, R. E., Di Francesco, P. and Zinn-Justin, P. 2013. A doubly-refined enumeration of alternating sign matrices and descending plane partitions. Journal of Combinatorial Theory, Series A 120(2), pp. 409-432. (10.1016/j.jcta.2012.09.004)
2012
- Behrend, R. E., Di Francesco, P. and Zinn-Justin, P. 2012. On the weighted enumeration of alternating sign matrices and descending plane partitions. Journal of Combinatorial Theory, Series A 119(2), pp. 331-363. (10.1016/j.jcta.2011.09.004)
2008
- Behrend, R. E. 2008. Osculating paths and oscillating tableaux. Electronic Journal of Combinatorics 15(1), article number: R7.
2007
- Behrend, R. E. and Knight, V. A. 2007. Higher spin alternating sign matrices. Electronic Journal of Combinatorics 14(1), article number: R83.
2004
- Behrend, R. E. and Evans, D. E. 2004. Integrable lattice models for conjugate An(1). Journal of Physics A Mathematical and General 37(8), pp. 2937-2947. (10.1088/0305-4470/37/8/006)
2001
- Behrend, R. E. and Pearce, P. A. 2001. Integrable and conformal boundary conditions for sl(2) A-D-E lattice models and unitary minimal conformal field theories. Journal of Statistical Physics 102(3/4), pp. 577-640. (10.1023/A:1004890600991)
2000
- Behrend, R. E., Pearce, P. A., Petkova, V. B. and Zuber, J. B. 2000. Boundary conditions in rational conformal field theories. Nuclear Physics B 579(3), pp. 707-773. (10.1016/S0550-3213(00)00225-X)
1998
- Behrend, R. E., Pearce, P. A. and Zuber, J. B. 1998. Integrable boundaries, conformal boundary conditions and A-D-E fusion rules [Letter]. Journal of Physics A: Mathematical and General 31(50), pp. L763-L770. (10.1088/0305-4470/31/50/001)
- Behrend, R. E., Pearce, P. A., Petkova, V. B. and Zuber, J. B. 1998. On the classification of bulk and boundary conformal field theories. Physics Letters B 444(1-2), pp. 163-166. (10.1016/S0370-2693(98)01374-4)
1997
- Behrend, R. E. and Pearce, P. A. 1997. Boundary weights for Temperley-Lieb and dilute Temperley-Lieb models. International Journal of Modern Physics B 11(23), pp. 2833-2847. (10.1142/S0217979297001386)
1996
- Behrend, R. E. and Pearce, P. A. 1996. A construction of solutions to reflection equations for interaction-round-a-face models. Journal of Physics A: Mathematical and General 29(24), pp. 7827-7835. (10.1088/0305-4470/29/24/009)
- Behrend, R. E. and Pearce, P. A. 1996. Reflection equations and exactly solvable lattice spin models. Czechoslovak Journal of Physics 46(12), pp. 1179-1187. (10.1007/BF01690331)
- Behrend, R. E., Pearce, P. A. and O'Brien, D. L. 1996. Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy. Journal of Statistical Physics 84(1-2), pp. 1-48. (10.1007/BF02179576)
Cynadleddau
- Behrend, R. E., Castillo, F., Chavez, A., Diaz-Lopez, A., Escobar, L., Harris, P. E. and Insko, E. 2023. Partial permutohedra. Presented at: 35th Conference on Formal Power Series and Algebraic Combinatorics, 17-21 July 2023, Vol. 89B.
- Behrend, R. 2018. An update on matters discussed at Oberwolfach by Ian Macdonald in May 1977 and David Robbins in May 1982. Presented at: Oberwolfach Workshop 1820, Oberwolfach, 13 - 19 May 2018Enumerative Combinatorics, Vol. 15. Oberwolfach Reports Vol. 23. European Mathematical Society pp. 1416-1418., (10.4171/OWR/2018/23)
Erthyglau
- Ayyer, A., Behrend, R. E. and Fischer, I. 2020. Extreme diagonally and antidiagonally symmetric alternating sign matrices of odd order. Advances in Mathematics 367, article number: 107125. (10.1016/j.aim.2020.107125)
- Ayyer, A. and Behrend, R. E. 2019. Factorization theorems for classical group characters, with applications to alternating sign matrices and plane partitions. Journal of Combinatorial Theory, Series A 165, pp. 78-105. (10.1016/j.jcta.2019.01.001)
- Behrend, R. E., Fischer, I. and Konvalinka, M. 2017. Diagonally and antidiagonally symmetric alternating sign matrices of odd order. Advances in Mathematics 315, pp. 324-365. (10.1016/j.aim.2017.05.014)
- Behrend, R. E., Fischer, I. and Konvalinka, M. 2016. Diagonally and antidiagonally symmetric alternating sign matrices of odd order. Discrete Mathematics and Theoretical Computer Science BC, pp. 131-142.
- Behrend, R. E., O, S. and West, D. B. 2015. Sharp lower bounds on the fractional matching number. Discrete Applied Mathematics 186, pp. 272-274. (10.1016/j.dam.2015.01.014)
- Behrend, R. E. 2014. Alternating sign matrix enumeration involving numbers of inversions and -1's, and positions of boundary 1's. RIMS Kokyuroku 1913, pp. 1-21., article number: 1.
- Behrend, R. E. 2013. Fractional perfect b-matching polytopes I: General theory. Linear Algebra and its Applications 439(12), pp. 3822-3858. (10.1016/j.laa.2013.10.001)
- Behrend, R. E. 2013. Multiply-refined enumeration of alternating sign matrices. Advances in Mathematics 245, pp. 439-499. (10.1016/j.aim.2013.05.026)
- Behrend, R. E., Di Francesco, P. and Zinn-Justin, P. 2013. A doubly-refined enumeration of alternating sign matrices and descending plane partitions. Journal of Combinatorial Theory, Series A 120(2), pp. 409-432. (10.1016/j.jcta.2012.09.004)
- Behrend, R. E., Di Francesco, P. and Zinn-Justin, P. 2012. On the weighted enumeration of alternating sign matrices and descending plane partitions. Journal of Combinatorial Theory, Series A 119(2), pp. 331-363. (10.1016/j.jcta.2011.09.004)
- Behrend, R. E. 2008. Osculating paths and oscillating tableaux. Electronic Journal of Combinatorics 15(1), article number: R7.
- Behrend, R. E. and Knight, V. A. 2007. Higher spin alternating sign matrices. Electronic Journal of Combinatorics 14(1), article number: R83.
- Behrend, R. E. and Evans, D. E. 2004. Integrable lattice models for conjugate An(1). Journal of Physics A Mathematical and General 37(8), pp. 2937-2947. (10.1088/0305-4470/37/8/006)
- Behrend, R. E. and Pearce, P. A. 2001. Integrable and conformal boundary conditions for sl(2) A-D-E lattice models and unitary minimal conformal field theories. Journal of Statistical Physics 102(3/4), pp. 577-640. (10.1023/A:1004890600991)
- Behrend, R. E., Pearce, P. A., Petkova, V. B. and Zuber, J. B. 2000. Boundary conditions in rational conformal field theories. Nuclear Physics B 579(3), pp. 707-773. (10.1016/S0550-3213(00)00225-X)
- Behrend, R. E., Pearce, P. A. and Zuber, J. B. 1998. Integrable boundaries, conformal boundary conditions and A-D-E fusion rules [Letter]. Journal of Physics A: Mathematical and General 31(50), pp. L763-L770. (10.1088/0305-4470/31/50/001)
- Behrend, R. E., Pearce, P. A., Petkova, V. B. and Zuber, J. B. 1998. On the classification of bulk and boundary conformal field theories. Physics Letters B 444(1-2), pp. 163-166. (10.1016/S0370-2693(98)01374-4)
- Behrend, R. E. and Pearce, P. A. 1997. Boundary weights for Temperley-Lieb and dilute Temperley-Lieb models. International Journal of Modern Physics B 11(23), pp. 2833-2847. (10.1142/S0217979297001386)
- Behrend, R. E. and Pearce, P. A. 1996. A construction of solutions to reflection equations for interaction-round-a-face models. Journal of Physics A: Mathematical and General 29(24), pp. 7827-7835. (10.1088/0305-4470/29/24/009)
- Behrend, R. E. and Pearce, P. A. 1996. Reflection equations and exactly solvable lattice spin models. Czechoslovak Journal of Physics 46(12), pp. 1179-1187. (10.1007/BF01690331)
- Behrend, R. E., Pearce, P. A. and O'Brien, D. L. 1996. Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy. Journal of Statistical Physics 84(1-2), pp. 1-48. (10.1007/BF02179576)
Gwefannau
- Behrend, R. E. 2024. Ehrhart polynomials of partial permutohedra. [Online]. arXiv. Available at: https://arxiv.org/abs/2403.06975
- Behrend, R. E., Fischer, I. and Koutschan, C. 2023. Diagonally symmetric alternating sign matrices. [Online]. arXiv: arXiv. (10.48550/arXiv.2309.08446) Available at: https://arxiv.org/abs/2309.08446
- Behrend, R. E., Castillo, F., Chavez, A., Diaz-Lopez, A., Escobar, L., Harris, P. E. and Insko, E. 2023. Partial permutohedra. [Online]. arXiv: arXiv. (10.48550/arXiv.2207.14253) Available at: https://arxiv.org/abs/2207.14253
- Behrend, R. E., O, S. and West, D. B. 2015. Sharp lower bounds on the fractional matching number. Discrete Applied Mathematics 186, pp. 272-274. (10.1016/j.dam.2015.01.014)
- Behrend, R. E. 2014. Alternating sign matrix enumeration involving numbers of inversions and -1's, and positions of boundary 1's. RIMS Kokyuroku 1913, pp. 1-21., article number: 1.
- Behrend, R. E. 2013. Fractional perfect b-matching polytopes I: General theory. Linear Algebra and its Applications 439(12), pp. 3822-3858. (10.1016/j.laa.2013.10.001)
- Behrend, R. E. 2013. Multiply-refined enumeration of alternating sign matrices. Advances in Mathematics 245, pp. 439-499. (10.1016/j.aim.2013.05.026)
- Behrend, R. E., Di Francesco, P. and Zinn-Justin, P. 2013. A doubly-refined enumeration of alternating sign matrices and descending plane partitions. Journal of Combinatorial Theory, Series A 120(2), pp. 409-432. (10.1016/j.jcta.2012.09.004)
- Behrend, R. E., Di Francesco, P. and Zinn-Justin, P. 2012. On the weighted enumeration of alternating sign matrices and descending plane partitions. Journal of Combinatorial Theory, Series A 119(2), pp. 331-363. (10.1016/j.jcta.2011.09.004)
Ymchwil
Meysydd ymchwil
- Combinatorics, gan gynnwys matricsau arwydd eiledol, graffiau, llwybrau dellt, parwydydd awyren a pholytopau.
- Ffiseg fathemategol, gan gynnwys theori maes cydffurfiol a modelau mecanyddol ystadegol integradwy.
Gwobr ymchwil
- Gwobr David P. Robbins Cymdeithas Mathemategol America 2019, gydag Ilse Fischer a Matjaž Konvalinka.
Cyllid ymchwil
- Grant Prosiect Ymchwil Ymddiriedolaeth Leverhulme RPG-2019-083, Mae'r combinatorics o matricsau arwydd eiledol a rhaniadau awyren.
Cydymaith ymchwil
Goruchwylio PhD cyfredol
Goruchwylio PhD diweddar
Sgyrsiau cynhadledd dethol
- Cydgysylltwyr Rhaglen Ymchwil Arbennig Algorithmig a Rhifol, 15 Mehefin 2018, Prifysgol Johannes Kepler Linz, Awstria.
- Gweithdy ar Gyfryngwyr Rhifol, 13–19 Mai 2018, Sefydliad Ymchwil Mathemateg, Oberwolfach, Yr Almaen.
- Algorithmig a Rhifiadol Cyfesurynnau Rhaglen Ymchwil Arbennig Colocwiwm , 16 Mawrth 2018, Prifysgol Fienna, Awstria.
- Combinatorics algebraidd a rhifiadol yn Okayama, 19–23 Chwefror 2018, Prifysgol Okayama, Japan.
- Rhaglen ar Gyfrifiadureg Algorithmig a Rhifol, 16 Hydref – 24 Tachwedd 2017, Sefydliad Rhyngwladol Mathemateg a Ffiseg Erwin Schrödinger, Fienna, Awstria.
- Rhaglen ar Fecaneg Ystadegol, Integreiddrwydd a Chyfesurynnau, 11 Mai – 3 Gorffennaf 2015, Sefydliad Galileo Galilei ar gyfer Ffiseg Ddamcaniaethol, Fflorens, yr Eidal.
- Rhaglen ar Gybinatoreg, Geometreg a Ffiseg, 2 Mehefin – 31 Gorffennaf 2014, Sefydliad Rhyngwladol Mathemateg a Ffiseg Erwin Schrödinger, Fienna, Awstria.
- Gweithdy ar gyfesurynnau algebraidd sy'n gysylltiedig â diagramau ifanc a ffiseg ystadegol, 6–10 Awst 2012, Sefydliad Rhyngwladol Astudiaethau Uwch, Kyoto, Japan.
- 68fed Séminaire Lotharingien de Combinatoire, 25–28 Mawrth 2012, Domaine Saint-Jacques, Ffrainc.
- Cyfarfod Lloeren StatPhys24 ar Gyfrifiadureg a Ffiseg Fathemategol, 12–14 Gorffennaf 2010, Prifysgol Queensland, Brisbane, Awstralia.
- Cyfarfod Coimbra ar 0-1 Matrics Theori a phynciau Cysylltiedig, 17–19 Mehefin 2010, Prifysgol Coimbra, Portiwgal.
- Rhaglen ar Gyffinyddion a Ffiseg Ystadegol, 1 Chwefror – 15 Mehefin 2008, Sefydliad Rhyngwladol Mathemateg a Ffiseg Erwin Schrödinger, Fienna, Awstria.
- Rhaglen ar Gybinatorics a Mecaneg Ystadegol, 14 Ionawr – 4 Gorffennaf 2008, Sefydliad Isaac Newton ar gyfer Gwyddorau Mathemategol, Caergrawnt, UK.
- 6ed Cynhadledd Ryngwladol ar Gyfryngwyr a Cheisiadau Llwybr Lattice, 12–14 Gorffennaf 2007, East Tennessee State University, Johnson City, UDA.
- 5ed Cynhadledd Patrymau Cymodi, 11–15 Mehefin 2007, Prifysgol St Andrews, UK.
- Colocwiwm Mathemateg Gregynog, 21–23 Mai 2007, Gregynog, DU.
- Gweithdy ar Broblemau Cyfryngol a godwyd gan Mecaneg Ystadegol, 19–23 Chwefror 2007, Centre de Recherches Mathématiques, Montréal, Canada.
- 6ed Gweithdy Bologna ar Ddamcaniaethau Maes Cydymffurfio a Modelau Integreiddio, 22–25 Medi 2004, Prifysgol Bologna, Yr Eidal.
Sgyrsiau adrannol dethol
- Prifysgol Technoleg Chalmers a Phrifysgol Gothenburg, Sweden, Adran Gwyddorau Mathemategol, 11 Mehefin 2019.
- Prifysgol Caerdydd, y DU, Ysgol Mathemateg, 20 Mawrth 2019.
- Prifysgol Queensland, Awstralia, Ysgol Mathemateg a Ffiseg, 14 Awst 2018.
- Prifysgol Dinas Llundain, y DU, Adran Mathemateg, 21 Mawrth 2017.
- Prifysgol De Cymru, y DU, yr Ysgol Cyfrifiadureg a Mathemateg, 26 Hydref 2016 .
- Prifysgol Melbourne, Awstralia, Adran Mathemateg ac Ystadegau, 11 Awst 2016.
- Queen Mary Prifysgol Llundain, y DU, Ysgol Gwyddorau Mathemategol, 11 Mawrth 2016.
- Prifysgol Glasgow, y DU, yr Ysgol Mathemateg ac Ystadegau, 18 Chwefror 2016.
- Maxwell Sefydliad y Gwyddorau Mathemategol, y DU, 17 Chwefror 2016.
- Royal Holloway University of London, UK, Adran Mathemateg, 2 Rhagfyr 2014.
- Prifysgol Glasgow, y DU, yr Ysgol Mathemateg ac Ystadegau, 13 Tachwedd 2012.
- Prifysgol Caint, y DU, yr Ysgol Mathemateg, Ystadegau a Gwyddor Actiwaraidd, 12 Mehefin 2012.
- Prifysgol Melbourne, Awstralia, Adran Mathemateg ac Ystadegau, 16 a 17 Mai 2011.
- Prifysgol Pierre a Marie Curie, Ffrainc, Labordy Ffiseg Ynni Damcaniaethol ac Uchel, 24 Mawrth 2011.
- Prifysgol Abertawe, y DU, Adran Fathemateg, 6 Tachwedd 2007.
- Prifysgol Melbourne, Awstralia, Adran Mathemateg ac Ystadegau, 6 Medi 2007.
- Y Brifysgol Agored, y DU, Adran Fathemateg, 8 Rhagfyr 2005.
- Prifysgol Caeredin, y DU, Ysgol Mathemateg, 8 Rhagfyr 2004.
- Prifysgol Efrog, y DU, Adran Fathemateg, 26 Mehefin 2003.
- Prifysgol Rhydychen, y DU, Sefydliad Mathemategol, 26 Chwefror 2002.
Ymweld â swyddi ymchwil
- Cyfadran Mathemateg, Prifysgol Fienna, Awstria, 1 Medi 2017 – 31 Awst 2018.
- Sefydliad Galileo Galilei ar gyfer Ffiseg Ddamcaniaethol, Fflorens, yr Eidal, 14 Mai – 6 Mehefin 2015.
- Sefydliad Rhyngwladol Mathemateg a Ffiseg Erwin Schrödinger, Fienna, Awstria, 8–21 Mehefin 2014.
- Sefydliad Rhyngwladol Mathemateg a Ffiseg Erwin Schrödinger, Fienna, Awstria, 8 Mai - 13 Mehefin 2008.
- Sefydliad Isaac Newton ar gyfer Gwyddorau Mathemategol, Caergrawnt, y DU, 14 Ionawr – 25 Ebrill 2008.
Rolau sy'n gysylltiedig ag ymchwil
- Cydlynydd yr Ysgol Mathemateg Colloquia.
- Adolygydd ar gyfer cyfnodolion ac asiantaethau ariannu.
- Arholwr PhD.
- Trysorydd Grŵp Ffiseg Mathemategol a Damcaniaethol, Sefydliad Ffiseg, 2012–2016.
- Gohebydd Sefydliad Isaac Newton, 2012–2017.
Sefydliad cynadleddau
- Cynhadledd Ryngwladol 31ain ar Gyfres Pŵer Ffurfiol a Combinatorics Algebraidd, Prifysgol Ljubljana, Slofenia, 1-5 Gorffennaf 2019.
- 29ain Cynhadledd Ryngwladol ar Gyfres Pŵer Ffurfiol a Rhwymiadureg Algebraidd, Prifysgol Queen Mary Llundain, DU, 9–13 Gorffennaf 2017.
- Gweithdy ar Ffiseg Gyneuol, Prifysgol Caerdydd, y DU, 17–19 Rhagfyr 2013.
Addysgu
Modiwlau a addysgir
- Dulliau mathemategol elfennol MA0017 I
- MA0122 Algebra I
- MA1008 Algebra Llinol I
- Dadansoddiad rhifiadol MA1700 I
- MA2014 Algebra I: Grwpiau
- Dadansoddiad rhifiadol MA2700 II
- Mecaneg Ystadegol MA0323
- MA3004 Combinatorics
- MA3014 Algebra II: Modrwyau
- Modiwl Darllen MA4901
Gwobr addysgu
- Darlithydd y Flwyddyn, 2016–2017.
Rolau sy'n gysylltiedig ag addysgu
- Dysgwr Blwyddyn 4.
- Siaradwr Diwrnod Agored Israddedig
- Cadeirydd Bwrdd Arholi Blwyddyn 2.
- Aelod o'r Panel Amgylchiadau Esgusodol.
Bywgraffiad
Cymwysterau
- BSc, Prifysgol Melbourne, Awstralia
- MSc, Coleg Imperial Llundain, UK
- PhD, Prifysgol Melbourne, Awstralia
Swyddi blaenorol
- Cymrawd Ymchwil, Sefydliad Ffiseg, Prifysgol Bonn, Yr Almaen
- Cymrawd Ymchwil, C. N. Yang Sefydliad Ffiseg Ddamcaniaethol, Prifysgol Stony Brook, UDA
