BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Melissa Sherman-Bennett (UC Berkely and Harvard University) DTSTART:20201006T150000Z DTEND:20201006T160000Z DTSTAMP:20260423T035536Z UID:OCAS/6 DESCRIPTION:Title: Man y cluster structures on positroid varieties\nby Melissa Sherman-Bennet t (UC Berkely and Harvard University) as part of Online Cluster Algebra Se minar (OCAS)\n\n\nAbstract\nEarly in the history of cluster algebras\, Sco tt showed that the homogeneous coordinate ring of the Grassmannian is a cl uster algebra\, with seeds given by Postnikov's plabic graphs for the\nGr assmannian. Recently the analogous statement has been proved for open Schu bert varieties (Leclerc\, Serhiyenko-SB-Williams) and more generally\, for open positroid varieties (Galashin-Lam). I'll\ndiscuss joint work with Ch ris Fraser\, in which we give a family of cluster structures on open Schub ert (and more generally\, positroid) varieties. Each of the cluster struct ures in this family has seeds given by face labels of relabeled plabic gra phs\, which are plabic graphs whose boundary is labeled by a permutation o f 1\, ...\, n. For Schubert varieties\, all cluster structures in this fam ily\nquasi-coincide\, meaning they differ only by rescaling by frozen vari ables and their cluster monomials coincide. In particular\, all relabeled plabic graphs for a Schubert variety give rise to seeds in the "usual" clu ster algebra structure on the coordinate ring. As part of our results\, we show the "target" and "source" cluster structures on Schubert varieties q uasi-coincide\, confirming a conjecture of Muller and Speyer. One proof to ol of independent interest is a permuted version of the Muller-Speyer twis t map\, which we use to prove many (open) positroid varieties are isomorph ic.\n LOCATION:https://researchseminars.org/talk/OCAS/6/ END:VEVENT END:VCALENDAR