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SUMMARY:Pierrick Bousseau (University of Georgia)
DTSTART;VALUE=DATE-TIME:20221118T200000Z
DTEND;VALUE=DATE-TIME:20221118T210000Z
DTSTAMP;VALUE=DATE-TIME:20230208T081010Z
UID:agstanford/98
DESCRIPTION:Title: Fock–Goncharov Dual Cluster Varieties and Gross–Siebert Mirrors\nby Pierrick Bousseau (University of Georgia) as part of Stanford algebr
aic geometry seminar\n\n\nAbstract\nCluster varieties are algebraic variet
ies obtained by gluing together complex tori using explicit birational tra
nsformations. They play an important role in algebra and geometric represe
ntation theory\, and have the peculiarity to come in pairs (A\,X). On the
other hand\, in the context of mirror symmetry\, associated with any log C
alabi–Yau variety is its mirror dual\, which can be constructed using th
e enumerative geometry of rational curves in the framework of the Gross–
Siebert program. I will explain how to bridge the theory of cluster variet
ies with the algebro-geometric framework of Gross–Siebert mirror symmetr
y and show that the mirror to the X-cluster variety is a degeneration of t
he Fock–Goncharov dual A-cluster variety and vice versa. To do this\, we
investigate how the cluster scattering diagram of Gross–Hacking–Keel
–Kontsevich compares with the canonical scattering diagram defined by Gr
oss–Siebert to construct mirror duals in arbitrary dimensions. This is j
oint work with Hulya Arguz.\n\nThe synchronous discussion for Pierrick Bou
sseau’s talk is taking place not in zoom-chat\, but at https://tinyurl.c
om/2022-11-18-pb (and will be deleted after ~3-7 days).\n
LOCATION:https://researchseminars.org/talk/agstanford/98/
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