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Victoria Schleis: Linear degenerate flag matroids and tropical flag varieties

Time: Wed 2023-04-19 10.15 - 11.15

Video link: Zoom meeting ID: 623 7437 7328

Participating: Victoria Schleis (University of Tübingen)

Abstract: Grassmannians and flag varieties are important moduli spaces in algebraic geometry. Their linear degenerations arise in representation theory as they describe quiver representations and their irreducible modules. As linear degenerations of flag varieties are difficult to analyze algebraically, we describe them in a matroidal setting and further investigate their tropical counterparts.

In this talk, I will introduce matroidal and tropical analoga of linear degenerate flags and their varieties obtained in joint work with Alessio Borzì and describe them in terms of morphisms of valuated matroids. Using techniques from matroid theory and linear tropical geometry, we use the correspondences between the different descriptions to gain insight on the structure of linear degeneration. For small examples, we relate observations on the tropical linear degenerate flag varieties to the flat irreducible locus studied in representation theory.