  We propose a robust a posteriori error estimator for the hybridizable
discontinuous Galerkin (HDG) method for convection-diffusion equations with
dominant convection. The reliability and efficiency of the estimator are
established for the error measured in an energy norm. The energy norm is
uniformly bounded even when the diffusion coefficient tends to zero. The
estimators are robust in the sense that the upper and lower bounds of error are
uniformly bounded with respect to the diffusion coefficient. A weighted test
function technique and the Oswald interpolation are key ingredients in the
analysis. Numerical results verify the robustness of the proposed a posteriori
error estimator. In numerical experiments, optimal convergence is observed.
