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Manoel Zanoelo Jarra (Universität Groningen)
2024-02-02 13:30 - 14:30 UTC | https://researchseminars.org/talk/TGiZ/59/
Title: Category of matroids with coefficients (https://researchseminars.org/talk/TGiZ/59/)
by Manoel Zanoelo Jarra (Universität Groningen) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z

Abstract
Matroids are combinatorial abstractions of the concept of independence in linear algebra. There is a way back: when representing a matroid over a field we get a linear subspace. Another algebraic object for which we can represent matroids is the semifield of tropical numbers, which gives us valuated matroids. In this talk we introduce Baker-Bowler's theory of matroids with coefficients, which recovers both classical and valuated matroids, as well linear subspaces, and we show how to give a categorical treatment to these objects that respects matroidal constructions, as minors and duality. This is a joint work with Oliver Lorscheid and Eduardo Vital.
