A matroid is a combinatorial object based on an abstraction of linear independence in vector spaces and forests in graphs. This talk connects matroid theory with algebra via the so-called von Staudt constructions. These are combinatorial gadgets to encode polynomials in matroids. I will discuss generalized matroid representations as arrangements over division rings, subspace arrangements and as entropy functions together with their relation to group theory. As an application this yields a proof that the conditional independence implication problem from information theory is undecidable. Based on joint work with Rudi Pendavingh and Geva Yashfe.

The homogenization of a conductive medium randomly perforated with inclusions of infi- nite conductivity is a well-known problem thanks to the work of Vassili Zhikov. However, the existence of an effective model is shown under assumptions on the interparticle dis- tance, which prevents the study of clusters and dense setting. In this talk of stochastic homogenization, we will provide a relaxed criterion ensuring homogenization relying on ideas from network approximation. This is joint work with David Gérard-Varet from Université Paris-Cité