Oligomorphic Groups and Tensor Categories

Explore the fascinating world of oligomorphic groups and tensor categories in this 52-minute lecture presented by Andrew Snowden from the University of Michigan. Delve into joint work with Nate Harman that attaches a symmetric tensor category to an oligomorphic group G equipped with a measure mu. Examine the simplest example involving the infinite symmetric group and its 1-parameter family of measures, resulting in Deligne's interpolation categories Rep(S_t). Discover how other choices for G lead to intriguing new categories, including the first semi-simple pre-Tannakian category in positive characteristic with superexponential growth and the first pre-Tannakian category with doubly exponential growth. Recorded on January 10, 2024, as part of IPAM's Symmetric Tensor Categories and Representation Theory Workshop at UCLA, this talk offers valuable insights for those interested in advanced mathematical concepts and their applications.