BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Man-Wai "Mandy" Cheung (Harvard) DTSTART:20200820T130000Z DTEND:20200820T140000Z DTSTAMP:20260423T041111Z UID:notts_ag/21 DESCRIPTION:Title: Polytopes\, wall crossings\, and cluster varieties\nby Man-Wai "Mand y" Cheung (Harvard) as part of Online Nottingham algebraic geometry semina r\n\n\nAbstract\nCluster varieties are log Calabi-Yau varieties which are a union of algebraic tori glued by birational "mutation" maps. Partial com pactifications of the varieties\, studied by Gross\, Hacking\, Keel\, and Kontsevich\, generalize the polytope construction of toric varieties. Howe ver\, it is not clear from the definitions how to characterize the polytop es giving compactifications of cluster varieties. We will show how to desc ribe the compactifications easily by broken line convexity. As an applicat ion\, we will see the non-integral vertex in the Newton Okounkov body of $ \\mathrm{Gr}(3\,6)$ comes from broken line convexity. Further\, we will al so see certain positive polytopes will give us hints about the Batyrev mir ror in the cluster setting. The mutations of the polytopes will be related to the almost toric fibration from the symplectic point of view. Finally\ , we can see how to extend the idea of gluing of tori in Floer theory whic h 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 wit h Bossinger\, Lin\, Magee\, Najera-Chavez\, and Vienna.\n LOCATION:https://researchseminars.org/talk/notts_ag/21/ END:VEVENT END:VCALENDAR