Douglas Lundholm: Recent rigorous studies of anyons and their number-theoretic aspects

As highlighted by this year's Nobel prize in physics, it is possible to create
exotic topological states of matter by confining quantum systems to planar
geometries. As an instance of this one may consider a one-parameter family of
emergent particles with unusual statistics, called anyons. These can be
modeled mathematically as ordinary identical particles (i.e. bosons or
fermions) in 2D with magnetic flux attached to them. I plan to review some
progress on our basic understanding of the anyon gas, focusing on lower bounds
to the energy by means of magnetic inequalities, which have been improved and
extended in recent joint work with Simon Larson. In the process we also learn
more about a dependence on certain number-theoretic properties of the anyonic
statistics parameter.