i'm going to explain the theorem of hopkins and miller (and partly goerss) that gives a version of lubin-tate deformation theory in the context of algebraic topology. more concretely, the theorem says that there is a functor $(k,\gamma) \mapsto e_{(k,\gamma)}$ from formal groups laws over perfect fields of characteristic $p>0$ to a very nice category of commutative ring spectra, namely $e_{\infty}$-ring spectra. it has the property that the formal group law of the cohomology theory associated with the ring spectrum $e_{(k,\gamma)}$ is the universal deformation of $(k,\gamma)$. by functoriality, we obtain an action of the (extended) morava stabilizer group on the spectrum $e_{(\mathbb{f}_{p^n},h_n)}$, where $h_n$ denotes the honda formal group law of height $n$. one application is the construction of the higher real $k$-theories $eo_n$ as the homotopy fixed point spectra obtained from the action of finite index subgroups of the morava stabilizer subgroup.