Title: Hyperfields, Ordered Blueprints, and Moduli Spaces of Matroids
Speaker: Matt Baker (Georgia Institute of Technology)
Abstract: In tropical geometry, linear spaces are in 1-1 correspondence with "valuated matroids". I will discuss a unified theory which views linear subspaces, ordinary matroids, and valuated matroids as special cases of “matroids over hyperfields”. I will then discuss the geometric construction of a "universal Grassmannian” which, via base change, yields (fine) moduli spaces for matroids over hyperfields. The universal Grassmannian is constructed using Oliver Lorscheid’s theory of ordered blueprints, which is also useful for understanding the relationship between Berkovich spaces, skeletons, and tropicalizations. This is joint work with Nathan Bowler and Oliver Lorscheid.
Seminar URL: https://research.math.osu.edu/gcis/
