Mathematical physics of anyons and topological states of matter

For quantum systems confined to lower-dimensional geometries there is a possibility to create states of matter that display very non-trivial topological behavior. The most famous example is the fractional quantum Hall effect and its associated effective particles with unusual statistics, called anyons. Despite such models having been studied intensively by physicists for a long time, there has been very little progress on the rigorous mathematical side. The aim of the workshop is therefore to bring together leading experts in the field, both mathematicians and physicists, to summarize the state of the art and to exchange ideas on future directions. In view of the serious theoretical intricacies of the field, particular emphasis will be put on the possible use of recent rigorous mathematics in physical applications.