BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Man-Wai Mandy Cheung (Harvard University) DTSTART:20201007T180000Z DTEND:20201007T190000Z DTSTAMP:20260423T040152Z UID:AG-Davis/7 DESCRIPTION:Title: Polytopes\, wall crossings\, and cluster varieties\nby Man-Wai Mandy Cheung (Harvard University) as part of UC Davis algebraic geometry seminar \n\n\nAbstract\nCluster varieties are log Calabi-Yau varieties which are a union 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 Vienna.\n LOCATION:https://researchseminars.org/talk/AG-Davis/7/ END:VEVENT END:VCALENDAR