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

Abstract:
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.