Tropical mirror symmetry for elliptic curves and beyond

Mirror symmetry for elliptic curves relates the generating series of Hurwitz numbers of the elliptic curve (i.e. counts of covers with fixed genus and simple branch points) to Feynman integrals. This is interesting, because quasimodularity properties of the generating series can be deduced, which is desirable to make statements about the asymptotics of the series. When passing to the tropical world, the relation works on a "fine level", i.e. summand by summand. We review the known results and then talk about generalizations: we can count covers in a broader context, and we can also count tropical curves in a product of an elliptic curve with the projective line. In both cases, the generating series in question can be related to Feynman integrals summand by summand. Joint work with Boehm, Bringmann, Buchholz, resp. with Boehm, Goldner.