CONICET | Buscador de Institutos y Recursos Humanos

Modular categories are algebraic models of anyons in two dimensional topological phases of matter where simple objects model anyons. In topological quantum computation, anyons give rise to quantum computational models. A classification of modular categories is important since it provides a classification of certain topological phases of matter. In this talk, we will give the definition of modular category and some basic examples of them. We will also introduce the notion of Frobenius-Perron dimension, which is a very useful invariant. A modular category with integral Frobenius-Perron dimension is called weakly integral. We will present some classification results of weakly integral modular categories of low rank.