From fractional quantum Hall effect to field-theoretic dualities

The fractional quantum Hall fluid is a paradigmatic topological state of matter. Many phenomena occurring in this fluid can be explained by postulating a new type of quasiparticle - the composite fermion. I will describe the new "Dirac composite fermion" theory, which has provided a simple solution to some long-standing puzzles and at the same time hast stimulated the discovery of a large number of new dualities in quantum field theory. I will also describe physical consequences of the new theory.