Abstract: A tensor category is a category with a notion of tensor product. The simplest example is the categories of finite dimensional vector spaces, or more generally the category of representations of a group. More exciting examples are the categories of representations of "quantum groups," which arise in various areas of mathematical physics. This talk will introduce the idea of a tensor category, and some of its variants (e.g. fusion/braided/modular tensor categories). I will also present the graphical formalism that allows you to compute things in tensor categories using pictures.

The talk will hopefully be accessible to graduate students who are interested in learning more about quantum topology. Being familiar with the basics of categories and group representations will be helpful.