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Séminaire de Géométrie

École polytechnique  – Salle de conférences du Centre de Mathématiques Laurent Schwartz


10h00 : Alex Fink (Queen Mary London)

"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.

In the first part of the talk, I'll provide relevant background in the theory of matroids and review their Hodge theory.

This talk is based on joint work with Chris Eur, Matt Larson and Hunter Spink.