| Given a triangulated category D, one can consider its space of stability conditions and a theory of Donaldson-Thomas (DT) invariants counting semistable objects. One of the conjectures of Mirror Symmetry leads to looking for geometric structures parametrized by the stability space, and a way of investigating these structures is by stating and solving a Riemann-Hilbert-Birkhoff boundary problem induced by the wall-crossing formula for DT data. In the case of a very simple DT theory, the solution to this problem is given in terms of Barnes multiple Gamma functions. Based on a joint work with T.Bridgeland and J.Stoppa. |