Particle-Vortex duality and Topological Quantum Matter

The past summer has seen an intense flurry of activity around the topic low-energy dualities that has uncovered a veritable web of 3-dimensional dualities relating a number of non-supersymmetric bosonic and fermionic theories. Moreover, these dualities find a very satisfying and direct “real-world” application to the physics of topological quantum matter. In this talk, I will give a more-or-less pedagogical introduction to the subject of low energy dualities and review some of the more recent developments in the field.