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.
Papers: I. Moffatt and E. Mphako-Banda, Handle slides for delta-matroids, preprint. (journal / arXiv)
T. Krajewski, I. Moffatt, A. Tanasa, Combinatorial Hopf algebras and topological Tutte polynomials, preprint. (journal / arXiv)
C. Chun, I. Moffatt, S. Noble and R. Rueckriemen, On the interplay between embedded graphs and delta-matroids, preprint.
I. Moffatt, Ribbon graph minors and low-genus partial duals, Annals of Combinatorics, to appear. (journal / arXiv)
Iain Moffatt and Johanna Strömberg, On the ribbon graphs of links in real projective space, Involve, 9-1 (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, preprint. (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, to appear. (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)
Unsigned state models for the Jones polynomial, Annals of
Combinatorics 15 (2011) 127-146. (journal / arXiv)
I. Moffatt and S.
Expansions for the Bollobás-Riordan and Tutte polynomials of
separable ribbon graphs, Annals of
Combinatorics 15 (2011) 675-706. (journal / arXiv)
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-trivial, Journal 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).
here for my papers on arXiv.
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.
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
from Spring 2008 AMS meeting at Baton Rouge