Abstracts
for the Seminar

Spring 2018

**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 F^{n} 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 F_{M}, F_{OM}, and F_{V} such that "subspaces of (F_{M})^{n}" are exactly matroids on the ground set [n], "subspaces of (F_{OM})^{n}" are exactly oriented matroids on the ground set [n], and "subspaces of (F_{V})^{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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