Graph representatives of positroid strata

Start: 03/30/2015 - 4:15pm
End  : 03/30/2015 - 5:15pm

Applied Math Seminar

Puck Rombach (UCLA)


This talk will be very accessible (including to grad students) and will involve juggling. 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. This is despite the fact that the matroid stratum dense in the positroid stratum does not typically contain such a representative (“positroids are not graphic matroids”). Joint work with Allen Knutson.

Kravis 102