Abstracts
for the Seminar

Fall 2014

**Speaker: ** Puck Rombach, UCLA

**Title: **Planar graphs represent all positroid strata

**Time:** 2:30 PM, Monday, December 1, 2014

**Place:** Malott 206

**Abstract:**
The positroid stratification, studied by many authors, is a coarsening of the matroid stratification of the Grassmannian. Each graph (with orientation and edge-ordering) gives a point in the Grassmannian; for a matroid stratum to contain such a point is a well-known forbidden minor condition on the matroid. We show that, by contrast, every positroid stratum contains a graphical representative; indeed, one can choose the graph to be planar. Joint work with Allen Knutson. The talk should be understandable with an elementary knowledge of graph theory.