# Mathematics Colloquia and Seminars

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### Operator-algebraic approach to topological phases

**Mathematical Physics & Probability**

Speaker: | Pieter Naaijkens, UC Davis - RWTH Aachen |

Location: | 1147 MSB |

Start time: | Wed, Oct 21 2015, 4:10PM |

I will consider the question of how one can determine if a quantum spin system exhibits topological order. One way this problem can be studied is through the use of operator algebraic methods. In this case, one studies the algebra of observables of the system and its representations. In this talk I will discuss a specific example of this. In particular, I will dicsuss how the Jones index of a certain inclusion of algebras can tell us something about the number of anyons in the system. I will also discuss how the construction can be interpreted in terms of physical operations. No in-depth knowledge of operator algebra will be assumed for this talk.