We review how supersymmetric quantum mechanics naturally leads to several
standard constructions in homological algebra. We apply these ideas to 2d Landau-Ginzburg
models with (2,2) supersymmetry to discuss wall-crossing. Some aspects of the web formalism
are reviewed and applied to the categorification of the Cecotti-Vafa wall-crossing formula for
BPS invariants. We then sketch the generalization to include twisted masses. In the final part of
the talk we sketch how some of these ideas give a natural framework for understanding a
recent conjecture of Garoufalidis, Gu, and Marino and lead to potentially new knot invariants.
The talk is based on work done with Ahsan Khan and recent discussions with Ahsan Khan, Davide
Gaiotto, and Fei Yan.