At the recent AMS sectional meeting in Las Vegas, Steven and Lenny gave talks about the augmentation category, and why it’s isomorphic to the sheaf category [NRSSZ].  Here are their slides:

Lenny’s talk: The augmentation category of a Legendrian knot

Steven’s talk: Augmentations are Sheaves

(I also gave a talk, but about moduli of objects in these categories — knotty character varieties — and didn’t make slides.)