University of Queensland mathematics colloquium on 2015-05-11.

Slides at https://prezi.com/r6w-yyxlispj/view

I'll explain the connection between quantum computation and topology, by analysing the computational complexity of the Jones polynomial. Recent discoveries in condensed matter physics potentially give us the tools to build quantum computers based on topological field theories. My research on topological field theories and the algebraic structures underlying them, particularly tensor categories and fusion categories, helps us understand which topological field theories may be accessible to experiment and engineering, and which can support quantum computation.