Wall-crossing formulas in algebra, geometry and physics

The wall-crossing formulas from the title appeared in my joint work with Maxim Kontsevich twice:

first time in the work on Homological Mirror Symmetry in 2004, and more recently and more systematically, in our
work on motivic Donaldson-Thomas invariants in 2008.
In quantum physics our invariants correspond to the so-called refined BPS invariants,
and the wall-crossing formulas describe jumps of the latter across walls of marginal stability.

In the first part of the talk I plan to overview basic notions (like e.g. the notion of stability data on a graded Lie algebra),
while in the second part I plan to discuss examples and applications, including the very recent ones.