Department of

October 2018 November 2018December 2018Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su MoTuWe Th Fr Sa 1 2 3 4 5 6 1 2 3 1 7 8 9 10 11 12 13 4 5 6 7 8 9 10 2 3 4 5 6 7 8 14 15 16 17 18 19 20 11 12 13 14 15 16 17 9 10 11 12 13 14 15 21 22 23 24 25 26 27 18 19 20 21 22 23 24 16 171819 20 21 22 28 29 30 31 25 26 27 28 29 30 23 24 25 26 27 28 29 30 31

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).