Relinde Jurrius: The q-analogue of a matroid

Abstract: In Combinatorics, a q-analogue is a generalization from finite sets to finite dimensional vector spaces, usually over a finite field. Before zooming in on q-matroids, the q-analogue of a matroid, we give some history and background on q-analogues.
We aim to develop some intuition on when a q-analogue is straightforward and when it is not: in general, an object defined using sets can have many equivalent descriptions that are not (at all) equivalent if we take their q-analogue. This means that for defining the q-analogue of a combinatorial object, it is sometimes needed to take a very elaborated and non-straightforward way to write its definition.
In this talk we illustrate these challenge with three notions associated to matroids: axioms for independent sets and bases; graphs; and some wild speculation about the q-analogue of polytopes.