Prefactorisation algebras for superselection sectors and topological order

In this talk I will explain the basics of topological order and superselection sector theory. The latter assigns a braided monoidal category to 2D topologically ordered quantum spin systems. The focus of this talk will be how this structure can be understood in terms of locally constant prefactorisation algebras over the category of cone-shaped regions. This naturally leads to a geometric origin for the braiding on the category of superselection sectors. Based on joint work with Marco Benini, Victor Carmona and Alexander Schenkel (arXiv:2505.07960).