Georgia Institute of Technology College of Sciences

We will look at various instances of how working with skeins (diagrams) provides a way to describe the existence of various topological quantum invariants that were originally described using representation theory. This provides a very simple description of these invariants. Along the way we will look at how to describe the algebraic data (ribbon categories) topologically and also how one could observe instances of certain dualities that exist between certain categories using these diagrams.