Quantum differential systems and some applications to mirror symmetry

Understand

We study mirror symmetry (A-side vs B-side) in the framework of quantum differential systems.

• We focuse on the logarithmic and non-resonant case, which describes the geometric situation.
• We show that quantum differential systems provide a good framework in order to generalize the construction of the rational structure on the A-side given by Katzarkov, Kontsevitch and Pantev for the projective spaces.
• As an application, we compute the rational structure obtained in this way on the orbifold cohomology of weighted projective spaces.