Mathematics

In the first part of the talk I will review some of the earlier examples of dualities among quantum field theories in three dimensions such as the particle-vortex duality and the level-rank duality. This is aimed to serve as an introduction to the subject. I will then move on to some of the more recent developments generalizing the aforementioned dualities as well as various checks that have so far been performed. I will close with a discussion on the challenges ahead towards proving some of the conjectures.