RO(G)-graded homotopy fixed point spectral sequence for height 2 Morava E-theory

The homotopy fixed points of Lubin-Tate theories are central objects in chromatic homotopy theory, as they are building blocks of $K(n)$-local spheres. This talk will describe the use of equivariant structure and vanishing line result to compute the $RO(Q_8)$-graded homotopy fixed points spectral sequence at height 2 and prime 2. This is joint work with Zhipeng Duan, Hana Jia Kong, Guchuan Li, and Guozhen Wang.