Algebra and Algebraic Geometry Special Seminar - Allen Knutson - The commuting scheme and pipe dreams
Title: The commuting scheme and pipe dreams
Abstract: The matrix equation X^2=0 implies the linear equation Trace(X)=0, but only set-theoretically not ideal-theoretically. Hochster asked in 1984 whether the equations XY=YX have similarly nonobvious implications. I'll describe some degenerations of these equations, that don't yet answer this question but do let one compute the degree of the "commuting scheme" defined by these equations, as a sum over "generic pipe dreams". Then I'll explain how these let one recover both the ordinary and bumpless pipe dream formulae for double Schubert polynomials. This work is joint with Paul Zinn-Justin.
Location: Hamilton Hall 104