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Representing matroids over tracts

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If you have a question about this talk, please contact Johannes Carmesin.

I’ll explain a generalisation of the notion of representable matroids over fields which allows us to encode a number of important classes of matroids and the relationships between them in terms of simple algebraic objects generalising fields, called tracts, and the morphisms between them. This gives a unified treatment of representable, oriented, regular and valuated matroids. I will then explain how to turn simple algebraic facts about tracts into theorems about the corresponding matroid classes, such as that any binary orientable matroid is regular.

This talk is part of the Study group in Graph Theory, Topology and Algorithms series.

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