Graduate Student Seminar-Forbidden minor problems for matroids and polymatroids.

Date and Time: Tuesday, March 8, 1-2pm

Place: Zoom
Zoom link:https://gwu-edu.zoom.us/j/92957649236?pwd=YmZIYytSUVVwcU1RdjZHYkNFak10U…

Speaker:  Kevin Long, GWU

Title: Forbidden minor problems for matroids and polymatroids.

Abstract: Wagner's theorem states that a graph is planar if and only if it does not have a minor isomorphic to K_5 or K_3,3. Robertson and Seymour proved that in general, any minor-closed class of graphs can be characterized by a finite list of excluded minors. In this talk, I discuss similar problems for matroids. I'll give an introduction to matroids, generalize the notion of minors for matroids, and introduce some well-known classes of matroids and their excluded minors. I'll also discuss my own research with my advisor on extending such problems to polymatroids and their natural matroids.