Growth rate, congruences, and other qualitative aspects of counting real rational curves on real K3 surfaces

I intend to start from reminding our, with Rares Rasdeaconu, real version of the Yau-Zaslow formula for the number of complex ones, and then will discuss some asymptotic and arithmetical properties of the lower bounds provided by our formula. In particular, I will discuss
under what assumptions on the surface a certain abundance of real rational curves holds.