The theory of support varieties is a powerful tool for studying the structure of non-semisimple tensor categories. Despite being an active area of research for 40+ years, there are still many open questions. This talk will focus on their use in studying the representations of Lie superalgebras in positive characteristic. Support varieties in the graded setting have new features and provide new challenges. I'll discuss what is known as well as some questions I wish I knew how to answer.
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