Last year, Andrew Snowden (UofM) and Nate Harman (UGA) introduced a new way of constructing tensor categories. In the first part of the talk, I will demonstrate how the general theory works in a particular case of an infinite symmetric group. The technique generalizes and explains the well-known example of Deligne's categories Rep(S_t).

In the second part of the talk, we will explore arboreal tensor categories, a completely new series of tensor categories. I will draw similarities and emphasize differences with Deligne's categories and other previously studied tensor categories.

Everyone is welcome! (background in tensor categories is not necessary for understanding of the talk)