Joost Slingerland

Particles between 1D and 2D: Anyons, fusion rings and graphs

It has long been theoretically expected that two dimensional systems can harbour anyons - quasiparticles with exotic exchange statistics, which fall outside the usual classification of particles into bosons and fermions. Indirect experimental evidence for the existence of anyons has been gathered for decades, but recently, more direct evidence is also becoming available which appear to show detection of the statistics of anyons in fractional quantum Hall systems. In this talk I will attempt to describe some of the mathematics describing anyons. In particular I will present some recent results on fusion algebras and tensor categories, and explore the fusion and braiding of anyon-like particles restricted to move on a graph, a situation which may be physically realized using networks of quantum wires.