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Gross, Hacking, and Keel have constructed mirrors of log Calabi-Yau surfacesin terms of counts of rational curves. Using $q$-deformed scattering diagramsdefined in terms of higher genus log Gromov-Witten invariants, we constructdeformation quantizations of these mirrors and we produce canonical bases ofthe corresponding noncommutative algebras of functions.

Quantum mirrors of log Calabi-Yau surfaces and higher genus curve counting