Abstract: The hot nuclear medium that permeated the early universe can be studied experimentally with heavy-ion collisions and through various theoretical approaches. New or upgraded experiments turn our attention to hard processes and a more fine-grained resolution of this primordial state of matter. In this endeavor quarkonia, open heavy flavors, and jets turn out to be versatile probes, which are usually described through models based on resummed perturbative QCD, AdS, and effective field theories. The lattice provides nonperturbative input and constraints to such models.
In-medium bottomonia, the complex static quark-antiquark potential, as well as the heavy-quark momentum and the jet transverse momentum diffusion transport coefficients are key quantities where lattice gauge theory has recently achieved significant progress with major impact for heavy-ion phenomenology. I review these lattice results, relate them to phenomenological applications, and close with an outlook towards expectations for the next few years.