(aka mirror symmetry/related topics)

Usually Tuesdays 1:00-2:00pm on Zoom

Organized by Lev Borisov, Emanuel Diaconescu, and Chris Woodward

Tuesday, November 16, 2021, 1pm on Zoom

Title: Family Floer mirror and mirror symmetry for rank 2 cluster varieties

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.

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