Speaker: XiaoLin Danny Shi (Harvard)
Title: Real Orientations of Lubin--Tate Spectra.
Abstract: We show that Lubin--Tate spectra at the prime 2 are Real oriented and Real Landweber exact. The proof is an application of the Goerss--Hopkins--Miller theorem to algebras with involution. For each height n, we compute the entire homotopy fixed point spectral sequence for $E_n$ with its $C_2$-action by the formal inverse. We study, as the height varies, the Hurewicz images of the stable homotopy groups of spheres in the homotopy of these $C_2$-fixed points. Then, I will talk about the slice spectral sequence of a $C_4$-equivariant spectrum. This spectrum is a variant of the detection spectrum of Hill--Hopkins--Ravenel and is very closely related to the height 4 Lubin--Tate theory.