Augmentations and sheaves for knot conormals

Symplectic invariants of the conormal bundle of a knot are knot invariants. We study the relation of two such invariants: the augmentations of the Chekanov-Eliashberg dga, and the microlocal category of simple sheaves. In this talk, I will explain a bijective correspondence between the these invariants, whose underlining geometry is suggested by the Nadler-Zaslow correspondence in mirror symmetry.