BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Man-Wai Cheung (Harvard University) DTSTART:20201204T141500Z DTEND:20201204T151500Z DTSTAMP:20260422T172515Z UID:TGiZ/11 DESCRIPTION:Title: Po lytopes\, wall crossings\, and cluster varieties\nby Man-Wai Cheung (H arvard University) as part of Tropical Geometry in Frankfurt/Zoom TGiF/Z\n \n\nAbstract\nCluster varieties are log Calabi-Yau varieties which are a u nion of algebraic tori glued by birational "mutation" maps. Partial comp actifications of the varieties\, studied by Gross\, Hacking\, Keel\, and K ontsevich\, generalize the polytope construction of toric varieties. Howev er\, it is not clear from the definitions how to characterize the polytope s giving compactifications of cluster varieties. We will show how to descr ibe the compactifications easily by broken line convexity. As an applicati on\, we will see the non-integral vertex in the Newton Okounkov body of Gr (3\,6) comes from broken line convexity. Further\, we will also see certai n positive polytopes will give us hints about the Batyrev mirror in the cl uster setting. The mutations of the polytopes will be related to the almos t toric fibration from the symplectic point of view. Finally\, we can see how to extend the idea of gluing of tori in Floer theory which then ended up with the Family Floer Mirror for the del Pezzo surfaces of degree 5 and 6. The talk will be based on a series of joint works with Bossinger\, Lin \, Magee\, Najera-Chavez\, and Vianna.\n LOCATION:https://researchseminars.org/talk/TGiZ/11/ END:VEVENT END:VCALENDAR