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Tuesday, December 11, 2018

**Abstract:** In a series of two talks, I will address the question of determining the K(n)-local Spanier-Whitehead dual of the Lubin-Tate spectrum, equivariantly with respect to the action of the Morava stabilizer group. In the first talk, I will focus on the abstract dualizing module, and introduce the Linearization Conjecture, which makes a more tangible (and linear) guess for what this spectrum should be. In the second talk, I will discuss a proof of the Linearization Conjecture, when restricted to small finite subgroups of the Morava stabilizer. This is work in progress, joint with Beaudry, Goerss, and Hopkins. (Note: the second talk will be independent from the first.)