Recently there has been much interest in the wall-crossing properties of BPS invariants in physics, or Donaldson-Thomas invariants in mathematics, under changes of stability conditions. The Kontsevich-Soibelman and Joyce-Song formulae give a general prescription for the discontinuity of these invariants across the wall. I shall present two new (conjecturally equivalent) wall-crossing formulae, which follow by quantizing the moduli space of multi-centered black holes using localization methods.

LPTHE Université Pierre et Marie Curie