Classification of simple flops and variation of GIT

Though classification of flops remains very challenging in general, progress on classification of simple flops has been made by D. Li and A. Kanemitsu, focusing on their relation with Fano manifolds. Derived equivalence are conjectured for all, and remain open in many cases. I review this, and discuss approaches to proving new equivalences using variation of GIT, in joint work with Weilin Su.