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Canonical bases of cluster algebras via tropical geometry. September 25, 2012 (02:00 PM PDT - 03:00 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Mark Gross
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I will talk about ongoing work with Hacking, Keel and Kontsevich on an approach to constructing canonical bases of cluster algebras using ideas which originate in mirror symmetry. We use the technology of "scattering diagrams" and "broken lines". Scattering diagrams arose in work of Kontsevich and Soibelman to construct mirror pairs of K3 surfaces, but are now being applied much widely. In particular, seed datum for a cluster algebra generates a particularly nice scattering diagram, which incorporates but has more information than the cluster complex. Broken lines are then tropical objects in the scattering diagram whose enumeration can be used to produce canonical bases.

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