Accessibility statement

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, curriculum working groups of the IoP and MEI, the Education Committee of the LMS, and the Advisory Committee on Mathematics Education.

I am currently Chair of Correspondents for the INI and ICMS, and Publications Secretary of the LMS.

Departmental roles

Head of Department 2015-2021




I work mainly in mathematical physics and in operations research and military history, with other interests in forecasting and probability scoring and in mathematical biology.

Mathematical Physics: Integrable models in 1+1D, especially Yangians, quantum groups and related algebras. My career-favourite result is (with Gustav Delius and others) (i) the extension of Olshanskii's twisted Yangians from the linear group to arbitrary symmetric pairs of Lie algebras (g,h),  (ii) the identification of the resulting twisted Yangians Y(g,h) as the hidden symmetry of quantum integrable models when the bulk symmetry g is broken by a boundary to h, and  (iii) (with Vidas Regelskis) the discovery of such structures hidden in the D3, 5 and 7 branes of the AdS/CFT, 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 (York) and Charles Young (Herts). Most recently Allan Gerrard is now a JSPS Fellow and Brennen Fagan is a post-doc at the York Leverhulme Centre for Anthropocene Biodiversity.

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

Operations research and military history: Combat modelling, especially of asymmetric war;  modelling-informed historical perspectives on 20thC air and naval war; probability scoring and forecasting. See the pages of the York Historical Warfare Analysis Group.


Research group(s)

Mathematical Physics and Quantum Information 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; boundary symmetry in the Hubbard and related models; the nested algebraic Bethe ansatz.

My second research field is the mathematical modelling of warfare, especially to answer historical questions, mostly from 20th century wars. Possible research projects would be in this area and in the mathematical modelling of insurgent war, where I collaborate with academics at the US Naval Postgraduate School. I am also interested in probability scoring, forecast verification and geopolitical forecasting.


Current research students



  • Introduction to Applied Mathematics

Contact details

Professor Niall MacKay
Professor of Mathematics
Room G/N/108

Tel: +44 1904 32 3493