Recorded 08 January 2024. Alexandra Utiralova of the University of California, Berkeley, presents "Representations of general linear groups in the Verlinde category" at IPAM's Symmetric Tensor Categories and Representation Theory Workshop. Abstract: The Verlinde category Ver_p is the semisimplification of the category of finite-dimensional representations of Z/pZ in characteristic p. In arXiv:2107.02372 Coulembier, Etingof, and Ostrik showed that all pre-Tannakian categories of moderate growth with additional nice property (Frobenius exactness) admit a fiber functor into Ver_p. Consequently, the study of representations of affine group schemes in such categories reduces to studying representations of affine group schemes in Ver_p. I will talk about what is known about the category of representations of the affine group scheme GL(X) for an object X in Ver_p, about the highest weight structure on it, and will discuss some questions that yet remain unanswered. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/symmetric-tensor-categories-and-representation-theory/?tab=overview