Interactions between Algebraic Topology and Representation Theory by Toric Code

Toric code is an error correction code designed by Kitaev in late 1990’s, which contributes to the birth of topological quantum computation. The goal of these lectures is to introduce toric code and related mathematics. We will explain an interaction between low-dimensional topology and representation of Drinfeld double. Especially, we will encode several operations (e.g. braidings) on representations into topology and geometry on surfaces. If time allows, we will give an overview of how toric code arises from chain complexes, which will be the prequel of our talk at Tokyo-Seoul Conference on Oct 6.

These lectures will be fundamental and concrete. We hope that the audience are familiar with basic concepts of finite groups and Hopf algebras.

These lectures will be held from Oct 2 to Oct 4, each from 13:30 to 15:00, for a total of 3 lectures.

Oct 2 (mon) Introduction to toric code.
Oct 3 (tue) Introduction to non-abelian toric code.
Oct 4 (wed) Further studies on toric code.