Speaker: Laura Anderson, Binghamton University
Title: Matroids and Grassmannians over hyperfields
Time: 2:30 PM, Monday, March 5, 2018
Place: Malott 206
Abstract: A hyperfield is similar to a field, except that addition in a hyperfield may be multivalued. Surprisingly, the notion of a linear subspace of a vector space Fn generalizes well to the case when F is a hyperfield, and even more surprisingly, this generalization encompasses much of matroid theory. For instance, there are particular hyperfields FM, FOM, and FV such that "subspaces of (FM)n" are exactly matroids on the ground set [n], "subspaces of (FOM)n" are exactly oriented matroids on the ground set [n], and "subspaces of (FV)n" are exactly valuated matroids on the ground set [n].
I will give a short introduction to matroids over hyperfields (work largely due to Matt Baker and Nathan Bowler) and discuss some results of Jim Davis and myself on the topology of Grassmannians over hyperfields.
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