Iain
Moffatt
Research Interests
My primary research interests lie in combinatorics and also its
applications to knot theory (particularly to quantum knot and 3-manifold
invariants). I am especially interested in applying algebraic
combinatorics to attack substantial questions in knot theory, and in
exploring new combinatorial structures that arise from recent
developments in knot theory. Recently, I have been mainly working on
embedded graphs and their polynomials. In this direction, I am
particularly interested in generalizations of duality and and the
applications of these generalizations to graph polynomials and to knot
theory. You can find further information on my CV.
Teaching:
Spring '10 Math 320 Foundations of Math
Math 525 Graph Theory: Here is the course text (the first few chapters are available on google books).
To get an idea of what graph theory is all about (it has nothing to do
with the graphs you know from calculus), you can see an old (and
outdated) version of the text here. You might want to take a look at wikipedia too.
Fall '09 Math 125 Calculus 1
Spring '09 Math 125-104, Math 125-105
Fall '08 Math 320, Math 115
Publications:
- M. Loebl and I. Moffatt, A permanent formula for the Jones polynomial, preprint.
- Jo. Ellis-Monaghan and I. Moffatt, Twisted duality and polynomials of embedded graphs, preprint.
- I. Moffatt, A characterization of partially dual graphs, preprint.
- I. Moffatt, Partial duality and Bollobás and Riordan's ribbon graph polynomial, Discrete Mathematics, 310 (2010) 174-183.
- I. Moffatt,
Unsigned state models for the Jones polynomial, Annals of Combinatorics, to appear.
- I. Moffatt and S.
Huggett,
Expansions for the Bollobás-Riordan and Tutte polynomials of
separable ribbon graphs, Annals of Combinatorics, to appear.
- I. Moffatt,
Knot invariants and the Bollobás-Riordan polynomial of
embedded graphs, European Journal of
Combinatorics, 29 (2008) 95-107.
- M. Loebl and I. Moffatt,
The
chromatic polynomial of fatgraphs and its categorification,
Advances in Mathematics, 217 (2008) 1558-1587.
- 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.
- I. Moffatt, A
new proof that alternating links are non-trivial, Fundamenta Mathematicae, to appear.
- I. Moffatt, The
Århus Integral and the μ-invariants,
Journal of Knot Theory and its Ramifications, 15 (2006) 361-377.
Thesis:
I. Moffatt, Integration
and Conjugacy in Knot Theory, PhD thesis,
University of Warwick, (2005).
Click
here for my papers on arXiv.
Slides:
Slides
from Spring 2008 AMS meeting at Baton Rouge.
Slides from BCC 2009, St Andrews.
