Mon, June 1 3pm EST (8pm BST, 7am Tue NZST)
Iain Moffatt, Royal Holloway University
The Tutte polynomial of a delta-matroid and the world of graph polynomials
Zoom [email rose.mccarty ~at~ uwaterloo ~.~ ca if you need the password]
The classical Tutte polynomial is a polynomial-valued invariant of graphs and matroids, and is arguably the most important and best studied graph polynomial. It’s important not only because it encodes a large amount of combinatorial information about a graph, but also because of its applications to areas such as statistical physics (as the Ising and Potts models) and knot theory (as the Jones and homfly polynomials). Unsurprisingly, given its role in combinatorics, the Tutte polynomial has been extended to many different settings for many different purposes.
In this talk I’ll discuss an extension of the Tutte polynomial to delta-matroids. (Delta-matroids are a generalisation of matroids introduced by Bouchet and others in the 1980s.) I’ll describe some of the advantages of the delta-matroid setting over the classical matroid setting, as well as some of its limitations; some of the properties of the classical polynomial that extend to the new setting, and some that don’t seem to. Through this, I hope to convey where the delta-matroid polynomial fits in the world of graph polynomials, and why I think it is a particularly interesting generalisation of the Tutte polynomial.
I’ll not assume any familiarity with the Tutte polynomial or with delta-matroids.