Benjamin Schröter: Classes of matroids for which Tutte polynomials are universal valuative invariants

ABSTRACT:
There are many valuative invariants of matroids. Prominent examples are the Tutte polynomial and the \mathcal{G}-invariant. The relevance of the \mathcal{G}-invariant steams from its universal property that any other valuative invariant can be obtained as a specialization. Nevertheless, the most intense studied invariant of matroids is clearly the Tutte polynomial as it respects deletion and contraction. An interesting question therefore is on which minor and duality closed classes of matroids is the Tutte polynomial universal. In my talk I will give a complete answer to this question, but also point out new and unexplored directions.

This talk is based on work with Luis Ferroni.