Colloque des sciences mathématiques du Québec

21 janvier 2022 de 14 h 00 à 15 h 00 (heure de Montréal/HNE) Réunion Zoom

The commuting variety and generic pipe dreams

Colloque par 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.