Graph representatives of positroid strata

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

Category
Applied Math Seminar

Speaker
Puck Rombach (UCLA)

Abstract

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.

Where
Kravis 102