Recorded 12 January 2024. Dmitri Nikshych of the University of New Hampshire presents "Tannakian radical and mantle of a braided fusion category" at IPAM's Symmetric Tensor Categories and Representation Theory Workshop. Abstract: This is a report on a joint work with Jason Green. We define a Tannakian radical of a braided fusion category C as the intersection of its maximal Tannakian subcategories. The localization of C corresponding to the Tannakian radical (called the mantle) has a canonical central extension which is a complete invariant of C. We study the properties of this invariant and discuss how it can be used in the classification of braided fusion categories. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/symmetric-tensor-categories-and-representation-theory/?tab=overview