Counting special Lagrangian classes and semistable Mukai vectors for K3 surfaces

Motivated by the study of growth rate of the number of geodesics in flat surfaces with bounded lengths, we study generalizations of such problems for K3 surfaces. In one generalization, we give an upper bound on the asymptotics of the number of irreducible special Lagrangian classes in K3 surfaces with bounded period integrals. In another generalization, we give the leading term of the counting function of the number of semistable classes with bounded central charges for generic Bridgeland stability conditions on algebraic K3 surfaces.