Title: Matroids and Algebra
Abstract: A matroid is a combinatorial object based on an abstraction of linear independence in vector spaces and forests in graphs. I will discuss how matroid theory interacts with algebra via the so-called von Staudt constructions. These are combinatorial gadgets to encode polynomials in matroids.
A main application is concerned with generalized matroid representations over division rings, matrix rings and probability space representations together with their relation to group theory.
Based on joint work with Rudi Pendavingh and Geva Yashfe.