Niall MacKay



I was an undergraduate in Cambridge, a PhD student in Durham and a post-doc in Kyoto before returning to Cambridge, with fellowships at Queens' and then Pembroke colleges. In 1998 I moved to Sheffield as a lecturer, then on to York in 2000. 

I have served on various national committees including the councils of the ILTHE and HEA, the Education Committee of the LMS, and the Advisory Committee on Mathematics Education.

Departmental roles

Head of Department



Mathematical Physics: Integrable models in 1+1D, especially Yangians, quantum groups and related algebras. My career-favourite result is (with Gustav Delius and others) the extension of Olshanskii's twisted Yangians from gl_n to arbitrary symmetric pairs of Lie algebras (g,h),  the identification of the resulting twisted Yangians Y(g,h) as the hidden symmetry of integrable models with boundary, and (with Vidas Regelskis) the discovery of such structures hidden in the D3, 5 and 7 branes of the gauge/string correspondence.

Past project and PhD students include Georg Gandenberger, Ben Short, Barry Miller, Patrick Massot, Paul Melvin, Matt Ferguson, John Pinney (Imperial), Adele Taylor, Andreas Rocen and Vidas Regelskis, and post-docs Nikolai Kitanine (U of Burgundy), Ian Marquette  (Queensland),  Alessandro Torrielli (Surrey), Benoit Vicedo and Charles Young (both Herts).

Most of my publications in mathematical physics can be found here.

Since several people have expressed interest, here (with the author's permission) is the 2010 York MMath dissertation in which a proof is given of Theorem 8 of V. G. Drinfeld, 'Hopf algebras and the QYBE' (which omits the proof): H A Rocen, Yangians and their representations

Warfare modelling: Combat modelling, insurgencies, and modelling-informed historical perspectives on air and naval war. See the pages of the York Historical Warfare Analysis Group.

Scaling laws in biologyScaling of human body mass with height: the Body Mass Index revisited and Mass scale and curvature in metabolic scaling. Here's a semi-popular article for Mathematics Today.

Research group(s)

Mathematical Physics Research Group

York Historical Warfare Analysis Group

Available PhD research projects

I work principally on algebraic aspects of quantum integrability, and am happy to supervise students on the hidden symmetry algebras (typically Yangians and other 'quantum groups') of integrable models, their representations and particle content. Most projects are suitable for students with an MSc-level background in theoretical physics (including strings, supersymmetry, QFT etc.), but some are more algebraic and may be suitable for pure mathematicians with an interest in mathematical physics. Past and current students have worked on: boundary scattering in AdS/CFT; the Yang-Baxter equation and invariant tensors of exceptional Lie groups; twist-deformed manifolds and cosmology; conserved charges in supergroup sigma models; boundary scattering in principal chiral models; quantum affine Toda solitons.

My second research field is the mathematical modelling of warfare, especially in its historical context. Possible research projects would be in this area and in the mathematical modelling of counter-insurgent warfare.



  • Electromagnetism
  • Introduction to Applied Mathematics

Contact details

Prof. Niall MacKay
Professor of Mathematics and Head of Department
Room G/N/125

Tel: +44 1904 32 3493