Paul Zinn-Justin: Periodic pipe dreams for matrix positroid varieties

Speaker
Paul Zinn-Justin, University of Melbourne

Abstract
We revisit the “periodic pipe dream” lattice model of [FGSX25], giving it a full geometric interpretation in terms of new varieties called matrix positroid varieties. Defining these requires a novel feature: the infinite matrices are not simply periodic, but involve a twist by a diagonal matrix. Matrix positroid varieties are indexed by arbitrary juggling patterns, and we will briefly discuss their combinatorics. We then calculate their Chern–Schwartz–MacPherson classes using a multiparameter deformation of their characteristic cycles, which we then degenerate into a union of varieties indexed by periodic pipe dreams.