|Location:||MSRI: Simons Auditorium|
A number of generalizations of matroids have been introduced, which contain more information than the purely linear-algebraic data that matroids do. Some examples are Dress and Wenzel's _valuated matroids_ and D'Adderio and Moci's _arithmetic matroids_. This talk is propaganda for a definition: I will introduce a notion of matroid over any commutative ring, of which the foregoing objects are special cases. In the Dedekind domain case, we can prove structure theorems and define the analogue of the Tutte polynomial.
This is joint work with Luca Moci.