Algebraic combinatorics seminar - Anna Bertiger

Intersecting determinantal ideas

Abstract:

I will talk about a class of ideals whose generators are of the form "all of the size d minors of the northwest i by j portion of a matrix of variables." I'll talk about how these ideals and their generators lead to some nice combinatorics involving the antidiagonals of the determinants and how the combinatorics can be used to intersect these ideals. In other words, I'll explain how to make interesting combinatorics from algebra and then how to use the combinatorics to do algebra. I'll also say something about geometric reasons involving the flag manifold and group actions that this is an interesting class of ideals.