Transport and Connection to Heavy-ion Collisions via Heavy Flavor Probes

The heavy ion experiments in Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) are going through upgrade in the next five years, shifting their focus more on the hard processes in the new runs. One of the main goals is to draw a finer image for the quark gluon plasma (QGP). The heavy flavor probes , which witness the whole history of heavy ion collision are particularly sensitive to test the properties of QGP formed in such collisions. The lattice results for heavy flavor probes provide transport and phenomenological models crucial inputs to describe the experimental observations like the strong suppression of the nuclear modification factor $R_{AA}$ and the non-zero azimuthal anisotropy at low $p_T$. In the last two years we have seen significant advances in the lattice QCD studies of heavy flavor probes, including the in-medium quarkonium properties, the complex static quark-antiquark potential and the heavy quark diffusion from lattice simulations at nonzero temperature. These achievements substantially deepen our understanding of the fate of quarkonium, the screening/unscreening of the complex potential and the temperature and quark mass dependence of the heavy quark diffusion in thermal medium. In these proceedings, we review recent results and briefly discuss possible directions in these studies.