Family Floer mirror and mirror symmetry for rank 2 cluster varieties

Mandy Cheung (Harvard University)

21-Oct-2021, 18:50-19:50 (2 years ago)

Abstract: The Gross-Hacking-Keel mirror is constructed in terms of scattering diagrams and theta functions. The ground of the construction is that scattering diagrams inherit the algebro-geometric analogue of the holomorphic disks counting. With Yu-shen Lin, we made use this idea and gave first non-trivial examples of family Floer mirror. Then with Sam Bardwell-Evans, Hansol Hong, and Yu-shen LIn, we construct a special Lagrangian fibration on the non-toric blowups of toric surfaces that contains nodal fibres, and prove that the fibres bounding Maslov 0 discs reproduce the scattering diagrams. As a consequence, we can then illustrate the mirror duality between the A and X cluster varieties.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic


Geometry, Physics, and Representation Theory Seminar

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