Towards lower bounds for the number of real rational curves on K3 surfaces

Surprisingly, in a quite a number of real enumerative problems the number of real solutions
happens to satisfy high lower bounds. For the moment, such a phenomenon is rather deep
studied in the case of interpolation of real points on a real rational surface by real rational curves. In this talk,
based on a, joint with Rares Rasdeaconu, work in progress, I intend to show that a similar phenomenon should
hold in the case of counting rational curves on K3 surfaces. As in other similar situations, our lower bounds
are derived from a suitable sign count. Our approach is, indeed, an adaptation to the real situation
of one of the approaches employed by Yau and Zaslow in their seminal paper for counting complex rational curves on K3 surfaces.