Zusammenfassung für den Vortrag am 14.09.2022 (14:00 Uhr)Seminar on Nonlinear Algebra
Lukas Kühne (Universität Bielefeld, Germany)
Matroids, Algebra, and Entropy
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.
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.