Mock Modular Forms and Quantum Black Holes

I will explain the relation between mermorphic Jacobi forms, mock Jacobi
forms, and the wall-crossing phenomenon in certain problems in enumerative
geometry along with the physics context of quantum black holes in which they
arise.

Analysis of the generating functions for quantum degeneracies of a class of
black holes in string theory leads to an infinite family of meromorphic
Jacobi forms. This family (and another related one) in turn furnishes a
list of examples of mock modular and mock Jacobi forms. This list contains
many known mock modular forms including the mock theta functions of
Ramanujan, the generating function of Hurwitz-Kronecker class numbers, the
mock modular form conjecturally related to the Mathieu group M24, as well as
an infinite number of new examples.