Matroid and delta-matroid tautological classes

Relationships between matroids and the permutahedral toric variety are central to matroid Hodge theory. One might wish to generalise these relationships, and the Hodge theory, to delta-matroids, which are Coxeter type B objects. I'll introduce delta-matroids and present one such relationship, inspired by the work of Berget-Eur-Spink-Tseng. Its consequences include volume polynomial formulae and positivity results for invariants like the interlace polynomial. This talk is based on joint work with Chris Eur, Matt Larson and Hunter Spink.