BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Melissa Sherman-Bennett (UC Berkeley) DTSTART:20210527T180000Z DTEND:20210527T190000Z DTSTAMP:20260423T024612Z UID:AG-Davis/33 DESCRIPTION:Title: Cluster structures on subvarieties of the Grassmannian\nby Melissa S herman-Bennett (UC Berkeley) as part of UC Davis algebraic geometry semina r\n\n\nAbstract\nEarly in the history of cluster algebras\, Scott showed t hat the homogeneous coordinate ring of the Grassmannian is a cluster algeb ra\, with seeds given by Postnikov's plabic graphs for the Grassmannian. R ecently the analogous statement has been proved for open Schubert varietie s (Leclerc\, Serhiyenko-SB-Williams) and more generally\, for open positro id varieties (Galashin-Lam). I'll discuss joint work with Chris Fraser\, i n which we provide a family of cluster structures for each open positroid variety. Seeds for these cluster structures are given by relabeled plabic graphs\, a natural generalization of Postnikov's construction. I'll also e xplain how for Schubert varieties (and conjecturally in general)\, relabel ed plabic graphs give additional seeds for the standard" cluster structure . Towards the end\, I'll also discuss joint work with M. Parisi and L. Wil liams on the cluster structure of some subvarieties of Gr(2\, n) which ari se naturally in the study of the m=2 amplituhedron. These subvarieties are closely related to positroid varieties but their cluster structure has so me intriguing dissimilarities.\n LOCATION:https://researchseminars.org/talk/AG-Davis/33/ END:VEVENT END:VCALENDAR