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]

Abstract:
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. 

Mon, May 25 3pm EST (8pm BST, 7am Tue NZST)
Peter Nelson, University of Waterloo
Extensions and coextensions of cliques
Zoom [email rose.mccarty ~at~ uwaterloo ~.~ ca if you need the password]

Abstract:
The class of matroids that are a single extension or coextension of the cycle matroid of a complete graph is surprisingly rich. I will discuss some Ramsey-theoretic and enumerative results for these objects.

I’m happy to announce another seminar series many of our readers may be interested in, titled “Algebraic Matroids and Rigidity Theory”. It is at 10am EST on Thursdays and is organized by Daniel Bernstein. Please email him at [dibernst ~at ~ mit ~.~ edu] or [bernstein.daniel ~at~ gmail ~.~ com] to get on the mailing list and for the password.

We do not intend on having a talk on May 18 for Victoria Day :). Here’s the info for Rudi’s talk next week.

Mon, May 11 3pm EST (8pm BST, 7am Tue NZST)
Rudi Pendavingh, Eindhoven University of Technology
Counting valuated matroid types
YouTube
Corrected slides

Abstract:
If $M$ is a matroid with bases $\mathcal{B}$, then a valuation of $M$ is a function $\nu:\mathcal{B}\rightarrow \mathbb{R}$ satisfying the following symmetric exchange axiom:

• If $B, B’\in \mathcal{B}$ and $e\in B\setminus B’$, then there is an $f\in B’\setminus B$ so that $$\nu(B)+\nu(B’)\leq \nu(B-e+f)+\nu(B’+e-f)$$

The YouTube link has been added for last week’s talk. Here’s the announcement for next week.

Mon, May 4 3pm ET (8pm BST, 7am Tue NZST)
Nathan Bowler, Universität Hamburg
Quasi-graphic matroids
Youtube Link

Abstract:
I’ll talk about a couple of classes of matroids which sit between frame and lifted-graphic matroids: the biased graphic matroids, which sit between these classes in a sense introduced by Zaslavsky, and the slightly better behaved quasi-graphic matroids, which were recently introduced by Geelen, Gerards and Whittle. I’ll give a very concrete combinatorial descriptions of the quasi-graphic matroids and use this to derive a fairly clean characterisation of the biased graphic matroids. I’ll discuss a topological construction giving some nontrivial examples of quasi-graphic matroids and raise the question of whether most examples are constructed in essentially this way.