Quarkonium correlators and spectral functions at zero and finite temperature

We study quarkonium correlators and spectral functions at zero and finite temperature using the anisotropic Fermilab lattice formulation with anisotropy ξ=2 and 4. To control cut-off effects we use several different lattice spacings. The spectral functions were extracted from lattice correlators with maximum entropy method based on a new algorithm. We find evidence for the survival of $1S$ quarkonium states in the deconfined medium till relatively high temperatures as well as for dissolution of $1P$ quarkonium states right above the deconfinement temperature.