Project A7: Matroids, codes, and their $q$-analogues
Project A7 is situated at the crossroads of algebra and combinatorics in the context of matroids. Matroids are combinatorial structures based on an abstraction of linear independence in vector spaces and are by now ubiquitous objects in mathematics admitting, for instance, a synthetic Hodge theory stemming from algebraic geometry. The first part of the project is concerned with matroids and arrangements of hyperplanes in light of Terao's freeness conjecture. The second part aims to investigate $q$-analogues of matroids and Coxeter matroids together with their relationships to modern coding theory.