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  • Tuesday, December 11, 14:00, 7.527

    Tom Sutherland (Mainz), Scattering diagrams (after Bridgeland)

  • Abstract:
    Scattering diagrams arise in the context of toric degenerations, encoding data which allows for a reconstruction of a variety from its degeneration and equipping it with a canonical basis of so-called theta functions. Applied to cluster varieties associated to a quiver, it encodes certain information of the cluster algebra as well as a new basis containing the cluster variables.
    The aim of this talk is to give an overview of work of Bridgeland, who constructs a scattering diagram on a real slice of the space of stability conditions on a triangulated category. Applied to a certain 3-Calabi-Yau categorification of the cluster algebra this construction recovers the scattering diagram of the cluster variety, giving a representation theoretic interpretation to the canonical basis.
    No prior knowledge of scattering diagrams or stability conditions will be assumed.