BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jeffrey Hicks (U. Edinburgh) DTSTART:20220923T140000Z DTEND:20220923T150000Z DTSTAMP:20260423T021056Z UID:LAGARTOS/47 DESCRIPTION:Title: Realizability criteria in tropical geometry from symplectic geometry \nby Jeffrey Hicks (U. Edinburgh) as part of (LAGARTOS) Latin American Rea l and Tropical Geometry Seminar\n\n\nAbstract\nThe realizability problem a sks if a given tropical subvariety is the tropicalization of some algebrai c subvariety. Realizability is already an interesting question for curves in $\\mathbb {R}^3$\, where Mikhalkin exhibited a tropical curve of genus 1 which is non-realizable. In recent independent work\, Mak-Ruddat\, Mates si\, Mikhalkin\, and I show that for many examples of tropcial subvarieti es in $\\mathbb {R}^n$ there exists a Lagrangian lift. This is a Lagrangia n submanifold of $(\\mathbb {C}^*)^n$ whose image under the moment map app roximates a given tropical subvariety. In particular\, every smooth tropic al curve in $\\mathbb {R}^n$ can be lifted to a Lagrangian submanifold (in contrast to the algebraic setting!)\n\n \n\nIn this talk\, I'll discuss w hat it means to be a Lagrangian lift of a tropical curve. We will then loo k at what symplectic conditions on the resulting Lagrangian detect realiza bility of the underlying tropical curve. As an application\, we will prove that every tropical curve in a tropical abelian surface has a rigid-analy tic realization.\n LOCATION:https://researchseminars.org/talk/LAGARTOS/47/ END:VEVENT END:VCALENDAR