Symplectic scattering diagrams for Log Calabi-Yau Surfaces

Abstract: The pioneering work of Gross-Hacking-Keel studied the mirror symmetry for log Calabi-Yau surfaces proved that there exists a natural superpotential defined on the mirrors. The key intermediate product of the mirror construction are some combinatorial data called scattering diagrams. In this talk, I will explain the symplectic heuristic of the construction and mathematically how we retrieve the superpotentials and the scattering diagram from Lagrangian Floer theory. As corollaries, we prove a version of cluster mirror symmetry of rank two, a real analogue of 27 lines on cubic surfaces and a folklore conjecture "open Gromov-Witten invariants=log Gromov-Witten invariants. This is a joint work with Bardwell-Evans, Cheung and Hong.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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