Rank 0 Donaldson-Thomas invariants are the mathematical incarnation of the index counting BPS black holes with D4, D2 and D0 brane charges in type IIA string theory compactified on a Calabi-Yau threefold.
String dualities predict that generating series of these invariants (with fixed D4 and D2-brane charge) should transform as vector-valued mock modular forms under Moebius transformations of the fugacity associated to the D0-brane charge. On the other hand, recent work by Soheyla Feyzbakhsh and Richard Thomas shows that rank 0 DT invariants can be computed from rank 1 DT invariants, which are in turn related to higher genus Gromov-Witten invariants. Combining explicit versions of this relation established by Soheyla, and the direct integration method of Klemm et al to compute higher genus GW invariants, we provide striking checks of the (mock) modularity of rank 0 DTinvariants, or D4-D2-D0 indices, for one-parameter Calabi-Yau families such as the quintic threefold and other hypergeometric models. Time permitting, I will also discuss two-parameter models with torus or K3 fibrations.
Note: there will be a lunch break at around noon, and the talk and/or discussions will continue over lunch in the lecture hall.