  We present and analyze an a posteriori error estimator for a space-time
hybridizable discontinuous Galerkin discretization of the time-dependent
advection-diffusion problem. The residual-based error estimator is proven to be
reliable and locally efficient. In the reliability analysis we combine a
Peclet-robust coercivity type result and a saturation assumption, while local
efficiency analysis is based on using bubble functions. The analysis considers
both local space and time adaptivity and is verified by numerical simulations
on problems which include boundary and interior layers.
