the zakharov system is a quadratically coupled system of a schrödinger and a wave equation, which is related to the focussing cubic schrödinger equation. we consider the associated cauchy problem in the energy-critical dimension d=4 and prove that it is globally well-posed in the full (non-radial) energy space for any initial data with energy and wave mass below the ground state threshold. the result is based on a uniform strichartz estimate for the schrödinger equation with potentials solving the wave equation. a key ingredient in the non-radial setting is a bilinear fourier extension estimate. this is joint work with timothy candy and kenji nakanishi.