Origins and Impacts of High-Density Symmetry Energy

What is nuclear symmetry energy? Why is it important? What do we know about it? Why is it so uncertain especially at high densities? Can the total symmetry energy or its kinetic part be negative? What are the effects of three-body and/or tensor force on symmetry energy? How can we probe the density dependence of nuclear symmetry energy with terrestrial nuclear experiments? What observables of heavy-ion reactions are sensitive to the high-density behavior of nuclear symmetry energy? How does the symmetry energy affect properties of neutron stars, gravitational waves and our understanding about the nature of strong-field gravity? In this lecture, we try to answer these questions as best as we can based on some of our recent work and/or understanding of research done by others. This note summarizes the main points of the lecture.