Last year, Andrew Snowden (UofM) and Nate Harman (UGA) introduced a new way of constructing tensor categories out of (really) large groups. What’s important for this talk is that these large groups are automorphism groups of omega-categorical theories.

I will give a friendly introduction to the topic and then focus on the known examples of omega-categorical theories and tensorial measures on them. Over the course of introducing the examples, I will demonstrate a beginner-friendly approach to the measures which follows the language of finite structures of the given theory. Hopefully, the audience can give me an idea of how to think about the measures from a model-theoretic point of view!