A survey of (abelian) 3d mirror symmetry

ALGEBRAIC GEOMETRY & NUMBER THEORY SEMINAR

By now it is well known that dualities of 2d and 4d TQFTs, namely mirror symmetry and electric-magnetic duality,  organize great swaths of geometry, representation theory, and number theory. In this lecture I will provide an introduction to 3d mirror symmetry, which is a lesser known but equally important duality of 3d TQFTs associated to hyper-Kahler quotients. To keep things simple I will focus on the simplest such quotients, known variously as toric hyper-Kahler manifolds or hypertoric varieties.