Georgia Institute of Technology College of Sciences

The representations of quantum groups are important in topology, namely, they can be used to construct quantum invariants of links. This relationship goes both ways: for example, the equivariant tensor category of representations of $U_q(\mathfrak{sl}_2)$ can be understood as a category of tangles. We will discuss a landmark result by Kuperberg who constructed graphical calculuses which describe the representation theory of the rank-2 simple Lie algebras.