Recently, I am trying to study the various progress made on the Bondal-Orlov conjecture: Birational Calabi-Yau varieties $\implies$ Equivalent derived categories.
I have started reading the paper by Bridgeland to study the notion of stability, and while searching for more references for the problem, I have encountered various papers which use ideas like GIT wall-crossing, grade restriction windows, etc. I have never studied GIT thoroughly, and although I am aware that these ideas have a close connection to Homological Mirror symmetry, I have never tried to explore these techniques.
I would be really grateful if someone can suggest some introductory references for the derived category-GIT connection, the techniques mentioned above, and how they give equivalences of semi-orthogonal decompositions of derived categories. I would really want to study these notions so that I will be able to fully appreciate the papers tackling various problems arising in the intersection of Birational Geometry and Derived categories.
Thank you.