Stability conditions and Autoequivalences via Tits cone intersections

I will explain (1) that stability conditions for general Gorenstein terminal 3-fold flops can be described as a covering map over something reasonable, and (2) the autoequivalence group is much larger than you might naively expect! Basically, part of the description of stability conditions comes from the movable cone, and its image under tensoring by line bundles. Alas, there is much more. This extra stuff is not immediately "birational" information, and it is a bit mysterious, but it does have a very natural noncommutative interpretation. In the process of this, I'll describe some of the new hyperplane arrangements that arise, which visually are very beautiful. I will also explain some applications including: autoequivalences, a description of monodromy on the SKMS, and some applications to curve counting. This is a summary of various joint work with Will Donovan, Yuki Hirano, and Osamu Iyama.