Low Rank Symmetric Fusion Categories in Positive Characteristic

Explore the classification of symmetric fusion categories in positive characteristic through this 30-minute conference talk presented by Agustina Czenky from the University of Oregon. Delve into the properties of the second Adams operation on the Grothendieck ring and its implications for classification results. Discover why the Adams operation is never the identity for non-trivial symmetric fusion categories. Examine the relationship between the rank of non-super-Tannakian symmetric fusion categories and the field's characteristic. Apply these insights to understand the classification of all symmetric fusion categories of rank 3 and those of rank 4 with exactly two self-dual simple objects. Recorded on January 12, 2024, as part of IPAM's Symmetric Tensor Categories and Representation Theory Workshop at UCLA, this talk offers a deep dive into advanced mathematical concepts for researchers and enthusiasts in the field.