Douglas Lundholm

Quantum systems confined to planar geometries may exhibit
effective particles with unusual statistics, called anyons. These can be
modeled as identical particles (bosons or fermions) in 2D with magnetic
flux attached to them. I will review recent progress on the rigorous study
of the many-body quantum mechanics of such anyons. Notable results include
the self-adjoint description of the many-anyon Hamiltonian, leading-order
determination of the ground state energy for anyonic systems with an
odd-numerator rational statistics parameter by means of a local exclusion
principle, as well as a mean-field formulation for almost-bosonic anyons.
The talk will be based on work in collaborations with M. Correggi, R.
Duboscq, S. Larson, N. Rougerie and J. P. Solovej.