Generic pipe dreams and the commuting scheme

Abstract: Consider the equations XY=YX on a pair of matrices. Do these generate a prime ideal, or, are there secret equations that pairs of commuting matrices satisfy? Mel Hochster asked this in '84 and noone has answered it (past small matrix size). I'll degenerate this scheme into pieces indexed by "generic pipe dreams", thereby giving a formula for its degree as a sum of powers of 2, and use an associated formula to derive both the ordinary and bumpless pipe dream formulae for Schubert polynomials. This work is joint with Paul Zinn-Justin.

algebraic geometry

Audience: researchers in the topic

Comments: This is the second algebraic geometry seminar of the day. We will zip out to buy lunch in between, and enjoy lunchtime theater with this talk.

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com