Graduate Student Seminar-A hierarchy of matroid invariants and a new matroid construction

Abstract: Matroids are a combinatorial object generalizing the concept of independence. Examples of matroids are seen in graph theory and linear algebra, where independence describes being acyclic or linearly independent respectively. I will provide an introduction to matroid theory and talk about some matroid invariants, including the Tutte polynomial, a well known invariant that specializes to the chromatic polynomial of a graph. I will also introduce some new results describing a new matroid construction, which behaves nicely with respect to these invariants.