BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lara Bossinger (UNAM Oaxaca) DTSTART:20201204T153000Z DTEND:20201204T163000Z DTSTAMP:20260422T172515Z UID:TGiZ/12 DESCRIPTION:Title: Tr opical geometry of Grassmannians and their cluster structure\nby Lara Bossinger (UNAM Oaxaca) as part of Tropical Geometry in Frankfurt/Zoom TGi F/Z\n\n\nAbstract\nThe Grassmannain\, or more precisely its homogeneous co ordinate ring with respect to the Plücker embedding\, was found to be a c luster algebra by Scott in the early years of cluster theory. Since then\, this cluster structure was studied from many different perspectives by a number of mathematicians. As the whole subject of cluster algebras broadly speaking divides into two main perspectives\, algebraic and geometric\, s o do the results regarding Grassmannian. Geometrically\, the Grassmannian contains two open subschemes that are dual cluster varieties.\n\nInteresti ngly\, we can find tropical geometry in both directions: from the algebrai c point of view\, we discover relations between maximal cones in the tropi calization of the defining ideal (what Speyer and Sturmfels call the tropi cal Grassmannian) and seeds of the cluster algebra. From the geometric poi nt of view\, due to work of Fock--Goncharov followed by work of Gross--Hac king--Keel--Kontsevich we know that the scheme theoretic tropical points o f the cluster varieties parametrize functions on the Grassmannian.\n\nIn t his talk I aim to explain the interaction of tropical geometry with the cl uster structure for the Grassmannian from the algebraic and the geometric point of view.\n LOCATION:https://researchseminars.org/talk/TGiZ/12/ END:VEVENT END:VCALENDAR