By physical considerations, Huang, Katz and Klemm conjectured in 2015 that topological string partition functions for elliptic Calabi-Yau 3-folds are governed by certain Jacobi forms. This gives strong structure results for curve counting invariants of elliptic CY 3-folds. I will explain a mathematical approach to prove (part of) the HKK Conjecture. Our method is to construct an involution on the derived category and use wall-crossing techniques.  The talk is based on joint work with Georg Oberdieck.