For a weakly nonlinear classical system, the kinetic equation for waves governs the evolution of the occupation number of a given wavevector. It is like the Boltzmann equation, but for waves instead of particles. As has been known for half a century, in addition to thermal equilibrium, the kinetic equation has another stationary solution: a turbulent state, describing a cascade of energy. Wave turbulence is observed in a wide range of physical contexts, most notably in surface gravity waves in the ocean. Higher order terms in the kinetic equation, going beyond leading order in the nonlinearity, have never been computed. We describe a method, based on quantum field theory, for computing such terms. We show that higher order terms can exhibit UV divergences. We sum the most divergent diagrams (bubble diagrams) to derive a kind of renormalized kinetic equation. Based on 2203.08168, 2212.02555, and work in progress with G. Falkovich. If you are planning to attend, please send and email to pietro.benetti_genolini@kcl.ac.uk or alan.rios_fukelman@kcl.ac.uk so your name is added to the participants list in order to grant you access to the building.