Iain Moffatt

Department of Mathematics
Royal Holloway
University of London
Egham
Surrey
TW20 0EX
United Kingdom

image of email address

tel: +44 (0)1784 443081
office: McRea 0-11 (what3words: open.tubes.zebra)

Research Interests

Algebraic combinatorics, topological graph theory, and knot theory.

My research centres 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. My main current research interests lie in delta-matroid theory, structural ribbon graph theory, and graph polynomials.

Books:

J.A. Ellis-Monaghan and I. Moffatt, Handbook of the Tutte Polynomial and Related Topics, CRC Press, 2022. (errata)

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

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

Papers:

J. Ellis-Monaghan, I. Moffatt and S. Noble, A coarse Tutte polynomial for hypermaps, (preprint).

I. Moffatt, Constructing a Tutte polynomial for graphs embedded on surfaces, 2023 MATRIX Annals, to appear. (preprint)

I. Moffatt, S. Noble and M. Thompson, Tensor products of multimatroids and a Brylawski-type formula for the transition polynomial, preprint. (preprint)

S. Huggett and I. Moffatt, A Negami-type splitting formula for the Jones and ribbon graph polynomials, preprint.

C. Merino, I. Moffatt, and S. Noble, An activities expansion of the transition polynomial of a multimatroid, preprint.

C. Merino, I. Moffatt, and S. Noble, The critical group of a combinatorial map, preprint. (preprint)

I. Moffatt and M. Thompson, Deletion-Contraction and the Surface Tutte Polynomial, European Journal of Combinatorics, 118 (2024) Article 103933. (journal / arXiv )

J. Ellis-Monaghan, A. Goodall, I. Moffatt, S. Noble, and L. Vena, Irreducibility of the Tutte polynomial of an embedded graph, Algebraic Combinatorics 5 (2022) 1337-1351. (journal).

I. Moffatt, From matrix pivots to graphs in surfaces: touring combinatorics guided by partial duals, pp. 825-856, in European Congress of Mathematics Portoroz, 20-26 June, 2021, EMS Press (2023). (book)

I. Moffatt and S. Noble, Topological graph theory through matroid theory, Newsletter of the London Mathematical Society, 496 - September (2021) 29-33. (journal)

J.A. Ellis-Monaghan and I. Moffatt, The Tutte polynomial for graphs, 14-26, in Handbook of the Tutte Polynomial and Related Topics, CRC Press, 2022. (book / preprint)

J.A. Ellis-Monaghan and I. Moffatt, Skein polynomials and the Tutte polynomial when x = y, 266-283, in Handbook of the Tutte Polynomial and Related Topics, CRC Press, 2022. (book / preprint)

I. Moffatt and J. Oh, A 2-isomorphism theorem for delta-matroids, Advances in Applied Mathematics, 126 (2021) paper 102133. (journal / preprint)

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, 169 (2020) 255-297. (journal / preprint)

J. Ellis-Monaghan, L. Kauffman and I. Moffatt, Edge colourings and topological graph polynomials, The Australasian Journal of Combinatorics, 72 (2018) 290-305 (journal)

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. (journal)

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 Stromberg, 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 Poincare - 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, 50 (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 Poincare - 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 Bollobas 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 Bollobas-Riordan and Tutte polynomials of separable ribbon graphs, Annals of Combinatorics 15 (2011) 675-706. (journal / arXiv)

I. Moffatt, Knot invariants and the Bollobas-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-trivial, Journal of Knot Theory and its Ramifications 19 (2010) 821-828. (journal / arXiv)

I. Moffatt, The Aarhus Integral and the \mu-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.