Tuesday, Oct 19, 3pm ET (8pm BST, 8am Wed NZST)
Tara Fife, Queen Mary University of London
(Minimal) Tropical Basis for Matroids
Password: email shaylaredlin ~at~ gmail ~.~ com (The password is the same format as usual, but first instead of last.)
Counterintuitively, a tropical basis for a matroid is not a type of basis or even a collection of basis. Rather it is a type of subset of the circuit set of a matroid which uniquely determines the matroid. In this talk, we will start by introducing a purely combinatorial definition of (minimal) tropical basis for matroids. We will explore how this definition is equivalent to the standard (algebraic) definition of tropical basis for matroids, and we will discuss some preliminary results. No advanced algebra background is assumed. This is joint work with Yelena Mandelshtam.
Tuesday, Oct 5, 3pm ET (8pm BST, 8am Wed NZST)
Jagdeep Singh, Louisiana State University
$2$-Cographs and Binary Comatroids
The well-known class of cographs or complement-reducible graphs is the class of graphs that can be generated from $K_1$ using the operations of disjoint union and complementation. In this talk, we consider $2$-cographs, a natural generalization of cographs, and binary comatroids, a matroid analogue. We show that, as with cographs, both $2$-cographs and binary comatroids can be recursively defined. However, unlike cographs, $2$-cographs and binary comatroids are closed under induced minors. We consider the class of non-$2$-cographs for which every proper induced minor is a $2$-cograph and show that this class is infinite. Our main result for graphs finds the finitely many members of this class whose complements are also induced-minor-minimal non-$2$-cographs. In the matroid case, our main result identifies all binary non-comatroids for which every proper flat is a binary comatroid. This is joint work with James Oxley.
Tuesday, Sept 28, 3pm ET (8pm BST, 8am Wed NZST)
Jim Geelen, University of Waterloo
Is this Ramsey’s Theorem for Matroids?
For a simple matroid $M$ with no lines of length $l$ or more, if the rank of $M$ is sufficiently large (as a function of $l$) and we $2$-colour the elements of $M$, is there necessarily a monochromatic line? We discuss this and a good many related problems.
Tuesday, Sept 21, 3pm ET (8pm BST, 7am Wed NZST)
Zach Walsh, Louisiana State University
New lift matroids for group-labeled graphs
We present a new construction for matroid lifts and apply it to group-labeled graphs, generalizing a well-known construction of Zaslavsky.