Online talk: Zach Walsh

Mon, July 27, 3pm ET (8pm BST, 7am Tue NZST)
Zach Walsh, University of Waterloo
Quadratically Dense Matroids

The extremal function of a class of matroids is the function whose value at an integer $n$ is the maximum number of elements of a simple matroid in the class of rank at most $n$. We present a result concerning the role of group-labeled graphs in minor-closed classes of matroids, and then use it to determine the extremal function, for all but finitely many $n$, for the class of complex-representable matroids which exclude a given rank-2 uniform matroid as a minor. This talk will focus on our original motivation, and on the connection between group-labeled graphs and representable matroids.

This is joint work with Jim Geelen and Peter Nelson.

Online talk: Pascal Gollin

Mon, July 20, 3pm ET (8pm BST, 7am Tue NZST)
Pascal Gollin, Institute for Basic Science
Obstructions for bounded branch-depth in matroids

DeVos, Kwon, and Oum introduced the concept of branch-depth of matroids as a natural analogue of tree-depth of graphs. They conjectured that a matroid of sufficiently large branch-depth contains the uniform matroid $U_{n,2n}$ or the cycle matroid of a large fan graph as a minor. In this talk, I present a proof that matroids of sufficiently large branch-depth either contain the cycle matroid of a large fan graph as a minor or have large branch-width.

This is joint work with Kevin Hendrey, Dillon Mayhew and Sang-il Oum.

Online Talk: Federico Ardila

Mon, July 13, 3pm ET (8pm BST, 7am Tue NZST)
Federico Ardila, SFSU, U. de Los Andes
Geometry of Matroids

Matroid theory had its origins in linear algebra and graph theory, and it turns out to have deep connections with many other fields. With time, the geometric roots of the field have grown much deeper, bearing many new fruits. The interplay between matroid theory and algebraic geometry has recently led to the solution of long-standing combinatorial questions. Perhaps more importantly, it has opened up new and interesting research directions at the intersection of combinatorics, algebra, and geometry.

This talk will discuss my recent joint work with Graham Denham and June Huh, where we use ideas from Lagrangian geometry to prove Brylawski and Dawson’s conjectures on the log-concavity of the h-vector of a matroid. I will gear the talk towards a combinatorial audience, and assume no previous knowledge of algebraic geometry.