Résumé:

BPS indices encoding entropy of supersymmetric black holes in compactifications of Type II string theory on compact Calabi-Yau threefolds coincide with generalized Donaldson-Thomas invariants whose computation represents an outstanding problem. I'll show how this problem can be solved for a set of one-parameter threefolds by combining a direct integration of topological string, modular properties of rank 0 DT invariants counting D4-D2-D0 BPS states, and wall-crossing relations between rank 1 and rank 0 DT invariants. As a result, one obtains explicit (mock) modular functions encoding infinite sets of D4-D2-D0 BPS indices, which in turn can be used to generate new boundary conditions for the holomorphic anomaly equation of topological string allowing to overcome the limitations of the direct integration method.