  An important question in the study of N=2 supersymmetric string or field
theories is to compute the jump of the BPS spectrum across walls of marginal
stability in the space of parameters or vacua. I survey four apparently
different answers for this problem, two of which are based on the mathematics
of generalized Donaldson-Thomas invariants (the Kontsevich-Soibelman and the
Joyce-Song formulae), while the other two are based on the physics of
multi-centered black hole solutions (the Coulomb branch and the Higgs branch
formulae, discovered in joint work with Jan Manschot and Ashoke Sen). Explicit
computations indicate that these formulae are equivalent, though a
combinatorial proof is currently lacking.
