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Tuesday, November 13, 2018

**Abstract:** The Tate construction is a powerful tool in classical homotopy theory. I will begin by reviewing the Tate construction and surveying some of its applications. I will then describe an enhancement of the Tate construction to genuine equivariant homotopy theory called the ``parametrized Tate construction" and discuss some of its applications, including C_2-equivariant versions of Lin's Theorem and the Mahowald invariant, blueshift for Real Johnson-Wilson spectra (joint work with Guchuan Li and Vitaly Lorman), and trace methods for Real algebraic K-theory (work-in-progress with Jay Shah).