Quebec Mathematical Sciences Colloquium

January 21, 2022 from 14:00 to 15:00 (Montreal/EST time) Zoom meeting

The commuting variety and generic pipe dreams

Colloquium presented by Allen Knutson (Cornell University)

Nobody knows whether the scheme "pairs of commuting nxn matrices" is reduced. I'll show how this scheme relates to matrix Schubert varieties, and give a formula for its equivariant cohomology class (and that of many other varieties) using "generic pipe dreams" that I'll introduce. These interpolate between ordinary and bumpless pipe dreams. With those, I'll rederive both formulae (ordinary and bumpless) for double Schubert polynomials. This work is joint with Paul Zinn-Justin.