Georgia Institute of Technology College of Sciences

We introduce combinatorial B-matrices over ordered blueprints B, which are combinatorial analogues of matrices and correspond to "matroids with a fixed basis". This provides a unifying framework for the study of bimatroids, linking sets, and their valuated analogues.  We then introduce and study their corresponding moduli spaces and describe their relations to the moduli space of matroids, introduced by Baker and Lorscheid. Inspired by the underlying combinatorics in the classical case, this allows us to define several interesting functors between moduli spaces of matrices and moduli spaces of matroids, and, by extension, between moduli spaces of matroids of different ranks.

Parts of this talk are based on joint work in progress with Martin Ulirsch.