In this talk, I will discuss and analyze an SPDE which arises naturally in the context of Liouville quantum gravity. This SPDE is built to preserve the so-called Liouville measure which has been constructed recently on the two-dimensional sphere S^2 and the torus T^2 in the work by David-Kupiainen-Rhodes-Vargas. In its simplified form, the SPDE can be written as follows
$$
\partial_t X = \frac 1 2 \Delta X + e^{\gamma X} + \sqrt{2\pi} \xi
$$
It belongs to the broad class of singular stochastic PDEs (which includes KPZ, dynamical Phi^4 etc.) with some new features due to the presence of intermittence.