Title: Quantum mirrors, tropical curves and curve counting on surfaces
Abstract: Certain counts of rational curves in (log Calabi–Yau) surfaces can be read off from the geometry of the Gross–Hacking–Keel mirror to the surface. I will discuss a generalisation of this to higher-genus curves, whose counts can be extracted from the geometry of a deformation quantisation of this mirror via a combinatorial gadget called (quantum) scattering diagrams. The connection between these two sides goes through tropical geometry. This is joint work with Patrick Kennedy-Hunt and Ajith Urundolil Kumaran.