Richard P. Stanley Seminar in Combinatorics: Linkage axioms for generic tropical oriented matroids

Tropical oriented matroids are first developed by Ardila and Develin as a combinatorial abstraction of tropical hyperplane arrangements. These matroids have been of interest in the past few decades due to the bijective correspondence with subdivisions of products of two simplices, as well as many other geometric and combinatorial objects. In this talk we will present an overview of these objects and their relationships, including some recent developments in connecting them with linkage matching fields by Sturmfels and Zelevinsky. The talk is mainly based on the preprint arXiv:2506.11265.

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