Iain Moffatt

Photo of me Department of Mathematics
Royal Holloway
University of London
TW20 0EX
United Kingdom

image of email address

tel: +44 (0)1784 443081
fax: +44 (0)1784 430766
office: McRea 011 (what3words: open.tubes.zebra)

Research Interests

Algebraic combinatorics, topological graph theory, and knot theory.

My research centers on the interface of combinatorics and topology. I am particularly interested in the ways in which combinatorial and topological structures can be encoded in one another, and in exploiting such connections to solve hard problems in combinatorics and  topology. I work extensively with topological extensions of graph polynomials and constructions. I am especially interested in using the additional topological structure to gain new understandings of classical polynomials (such as the chromatic, Tutte and Penrose polynomials), their evaluations,  their connections between each other, and their connections with quantum  invariants of knots and  statistical mechanics.

I am also interested in in quantum and finite-type invariants of knots and applications of geometric group theory to knot theory. In addition, I have recently been working on applications of graph theory to biology.

Non-research Interests

Photo of me
Away from work, I like to swap math problems for bouldering problems.

(Me on the problem "Hung Out to Dry" (f5+) at the Cuttings, Portland.)


book cover

D.M. Jackson and I. Moffatt, An Introduction to Quantum and Vassiliev Knot invariants
, Springer, 2019.

book cover

J. Ellis-Monaghan and I. Moffatt, 
Graphs on surfaces: Dualities, Polynomials, and Knots, Springer, 2013. (errata)


I. Moffatt, Delta-matroids for graph theorists, Surveys in combinatorics 2019, 167-220, London Math. Soc. Lecture Note Ser., 446, Cambridge Univ. Press, Cambridge, 2019.  (book / preprint)

S. Huggett and I. Moffatt, Embedded graphs and their Tutte polynomials, Mathematical Proceedings of the Cambridge Philosophical Society, to appear. (journal / preprint)

J. Ellis-Monaghan, L. Kauffman and I. Moffatt, Edge colourings and topological graph polynomials, The Australasian Journal of Combinatorics, 72 (201) 290-30.5

C. Chun, R. Hall, C. Merino, I. Moffatt, and S. Noble, The structure of delta-matroids with width one twists, The Electronic Journal of Combinatorics,  25 (2018) P1.9. 

S. Garoufalidis, I. Moffatt, and D. Thurston, Non-peripheral ideal decompositions of alternating knots, preprint.
(journal / arXiv)

I. Mofffatt and B. Smith, Matroidal frameworks for topological Tutte polynomials, Journal of Combinatorial Theory Series B, 133 (2018)  1-31.
(journal / preprint)

I. Moffatt and E. Mphako-Banda,
Handle slides for delta-matroids, European Journal of Combinatorics, 59 (2017) 23-33. (journal / arXiv)

T. Krajewski, I. Moffatt, A. Tanasa, Hopf algebras and Tutte polynomials,
Advances in Applied Mathematics, 95 (2018) 271-330. (journal / arXiv)

C. Chun, I. Moffatt, S. Noble and  R. Rueckriemen,
On the interplay between embedded graphs and delta-matroids, Proceedings of the London Mathematical Society, 118 (2019) 675-700. (journal / arXiv)

I. Moffatt, Ribbon graph minors and low-genus partial duals, Annals of Combinatorics, 20 (2016) 373-378. (journal / arXiv)

Iain Moffatt and Johanna Strömberg, On the ribbon graphs of links in real projective space, Involve, 9 (2016) 133-153. (journal / arXiv)

J. Ellis-Monaghan and I. Moffatt,
A note on recognizing an old friend in a new place: list coloring and the zero-temperature Potts model, Annales de l'Institut Henri Poincaré - D, 1 (2015) 429-442. (journal / arXiv)

C. Chun, I. Moffatt, S. Noble and  R. Rueckriemen,
Matroids, Delta-matroids and Embedded Graphs, Journal of Combinatorial Theory, Series A, 167 (2019) 7-59. (journal / arXiv)

J. Ellis-Monaghan and I. Moffatt,
The Las Vergnas Polynomial for embedded graphs, European Journal of Combinatorics, 5
0 (2015) 97-114. (journal / arXiv)

I. Moffatt, Excluded minors and the graphs of knots, Journal of Graph Theory, 81 (2016) 329-341. (journal / arXiv)

M. Klazar, M. Loebl, and I. Moffatt, The Potts model and chromatic functions of graphs, Annales de l'Institut Henri Poincaré - D, 1 (2014) 47-60. (journal / arXiv)
J. Ellis-Monaghan, A. McDowell, I. Moffatt and G. Pangborn, DNA origami and the complexity of Eulerian circuits with turning costs, Natural Computing, 14 (2015) 491-503.
(journal / arXiv)

J. Ellis-Monaghan and I. Moffatt,
Evaluations of topological Tutte polynomials, Combinatorics, Probability and Computing, 24 (2015) 556-583. (journal / arXiv)

I. Moffatt, Separability and the genus of a partial dual, European Journal of Combinatorics 34 (2013) 355-378. (journal / arXiv)

L. McDonald and I. Moffatt, On the Potts model partition function in an external field, Journal of Statistical Physics, 146 (2012) 1288-1302. (journal / arXiv)

J. Ellis-Monaghan and I. Moffatt,
A Penrose polynomial for embedded graphs, European Journal of Combinatorics 34 (2013) 424-445. (journal / arXiv)

S. Huggett and I. Moffatt, Bipartite partial duals and circuits in medial graphs, Combinatorica 33 (2013) 231-252. (journal / arXiv)

S. Huggett, I. Moffatt and N. Virdee, On the Seifert graphs of a link diagram and its parallels, Mathematical Proceedings of the Cambridge Philosophical Society, 153 (2012) 123-145. (journal / arXiv)

I. Moffatt, Partial duals of plane graphs, separability and the graphs of knots, Algebraic and Geometric Topology, 12 (2012) 1099-1136. (journal / arXiv)

J. Ellis-Monaghan and I. Moffatt, The Tutte-Potts connection in the presence of an external magnetic field, Advances in Applied Mathematics, 47 (2011) 772-782. (journal / arXiv)

M. Loebl and I. Moffatt,  A permanent formula for the Jones polynomial, Advances in Applied Mathematics 47 (2011) 659-667. (journal / arXiv)

J. Ellis-Monaghan and I. Moffatt, Twisted duality for embedded graphs, Transactions of the American Mathematical Society, 364 (2012) 1529-1569. (journal / arXiv)

I. Moffatt, A characterization of partially dual graphs, Journal of Graph Theory 67 (2011), 198-217. (journal / arXiv)

I. Moffatt, Partial duality and Bollobás and Riordan's ribbon graph polynomial, Discrete Mathematics 310 (2010) 174-183. (journal / arXiv)

I. Moffatt, Unsigned state models for the Jones polynomial, Annals of Combinatorics 15 (2011) 127-146. (journal / arXiv)

I. Moffatt and S. Huggett, Expansions for the Bollobás-Riordan and Tutte polynomials of separable ribbon graphsAnnals of Combinatorics  15 (2011) 675-706. (journal / arXiv)

I. Moffatt, Knot invariants and the Bollobás-Riordan polynomial of embedded graphs, European Journal of Combinatorics 29 (2008) 95-107. (journal / arXiv)

M. Loebl and I. Moffatt, The chromatic polynomial of fatgraphs and its categorification, Advances in Mathematics 217 (2008) 1558-1587. (journal / arXiv)

D. M. Jackson, I. Moffatt and A. Morales, On the group-like behaviour of the Le-Murakami-Ohtsuki invariant, Journal of Knot Theory and its Ramifications 16 (2007) 699-718. (journal / arXiv)

I. Moffatt, A new proof that alternating links are non-trivialJournal of Knot Theory and its Ramifications 19 (2010) 821-828. (journal / arXiv)

I. Moffatt, The Ċrhus Integral and the μ-invariants, Journal of Knot Theory and its Ramifications 15 (2006) 361-377. (journal / arXiv)

I. Moffatt, Integration and Conjugacy in Knot Theory, PhD thesis, University of Warwick, (2005). (arXiv)

Click here for my papers on arXiv.

Editorial Work

From 2016-19, I was the Editor-in-Chief of the Newsletter of the London Mathematical Society, the UK's learned society for mathematics. I took the Newsletter through a major redesign, bringing in a new format and adding new feature content.

I recently guest edited a special issue of Advances in Applied Mathematics on the Tutte Polynomial.

Conferences organised:  

Comparative Theory for Graph Polynomials,  Dagstuhl Seminar, September 29 – October 4 , 2019
FPSAC 17, London 2017
Graph Polynomials: Towards a Comparative Theory, Dagstuhl Seminar,  12th-17th June 12 – 17 2016.
Workshop on New Directions for the Tutte Polynomial:  Extensions, Interrelations, and Applications, Royal Holloway University of London, 11th-14th July 2015.
Special session on graph polynomials and their applications, CGTC46, 2nd-6th March 2015.


Slides from Eindhoven 2016
Slides from Dagstuhl 2016
Slides from Fields 2016
Bordeaux 2015: slides, problems, ribbon graphs, polynomials 1, duality, medial graphs, polynomials 2, knots, matroids.
Slides from
BCC 2015, Warwick
Slides from
Spring 2012 meeting in Vermont
Slides from Spring 2012 AMS meeting at Tampa
Slides from Fields Undergraduate talk

Slides from SIAM DM10 meeting in Austin
Slides from BCC 2009, St Andrews
Slides from Spring 2008 AMS meeting at Baton Rouge