Explore the intricacies of support varieties in representation theory through this 48-minute lecture by Sarah Witherspoon from Texas A&M University. Delve into the application of support varieties as crucial tools in representing finite groups and finite group schemes, and discover how the theory extends to finite tensor categories. Focus on the tensor product property for support varieties and its reduction to indecomposable periodic objects. Gain insights into the implications of this reduction, including the validity of the tensor product property for all symmetric finite tensor categories over algebraically closed fields of characteristic 0. Learn about the collaborative research behind these findings and broaden your understanding of symmetric tensor categories and representation theory.