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Monday, November 11, 2019

**Abstract:** Picard groups have been classically studied in commutative algebra and algebraic geometry. These can be suitably generalised to define picard groups of $\mathbb{E}_{\infty}$ ring spectra. In this situation a natural question to ask is "How is the picard group of $R$ related to the picard group of $R_*$?". In this expository talk, I will explain some methods which have been used to answer the above question.