The 1 + 1 dimensional Kardar-Parisi-Zhang equation: More surprises

In its original version, the KPZ equation models the dynamics of an interface bordering a stable phase against a metastable one. Over the past few years the corresponding two-dimensional field theory has been applied to models with different physics. Out of a wide choice, the spin-spin time correlations for the Heisenberg chain will be discussed at some length, also the equilibrium time correlations of the conserved fields for 1D fluids. An interesting recent theoretical advance is the construction of the scale-invariant asymptotic theory, the so-called KPZ fixed point.