Research Seminar: Complex Geometry

22.11.2017 Pierrick Bousseau (Imperial College)

Quantum mirrors of log Calabi-Yau surfaces

Abstract: I will start describing the Gross-Hacking-Keel realization of mirror symmetry for log Calabi-Yau surfaces: the mirror variety is constructed by gluing elementary pieces together according to some gluing functions determined by counting rational curves in the original variety. I will then explain how to construct non-commutative deformations of these mirrors by including contributions of counts of higher genus curves in the original variety.