Recent Developments in Lattice Studies for Quarkonia

After discussing results of dilepton rates and electrical conductivity obtained from continuum extrapolated results of light quark correlation functions in quenched QCD I will give a review on recent developments in lattice QCD studies for quarkonia in the quark gluon plasma medium. Recent progress in the extraction of spectral properties from lattice QCD calculations of hadronic correlation functions will be discussed. Besides medium modifications of bound states and their dissociation in the plasma I will focus on transport coefficients, like heavy quark diffusion constants extracted from different correlation functions on the lattice. Present limitations and future perspectives for studies of quarkonia and related transport coefficients on the lattice will be discussed. See also [B. Muller, these proceedings, arXiv:1207.7302; C. Gale, these proceedings, arXiv:1208.2289; A. Rothkopf, these proceedings, arXiv:1207.5486; H.-T. Ding, arXiv:1207.5187] for recent overviews and related discussions of those topics.