BPS indices encoding the entropy of supersymmetric black holes in compactifications of Type II string theory on Calabi-Yau threefolds, known in mathematics as generalized Donaldson-Thomas invariants, possess remarkable (mock) modular properties. I'll explain the physical origin of mock modularity and show, for a set of one-parameter threefolds, how it can be used, together with wall-crossing and direct integration of topological string, to compute generating functions of D4-D2-D0 BPS indices. This in turn provides new boundary conditions for the holomorphic anomaly equation on the topological string partition function allowing to overcome the limitations of the direct integration method. In the end, I'll present prelimenary results on the asymptotic growth of DT invariants, hinting for the existence of some phase transitions, and a new approximate formula for Gopakumar-Vafa invariants.
Zoom link: https://icts-res-in.zoom.us/j/88092766911?pwd=R3ZrVk9yeW96ZmQ4ZG9KRzVhenRKZz09
Meeting ID: 880 9276 6911
Passcode: 232322