Equation of State and Net-charge Fluctuations for Strongly-interacting Matter

Exploration of the phase diagram of Quantum Chromodynamics (QCD) matter is an exciting undertaking that will elucidate the underlying fundamental theory of the strong nuclear force. The strong force, one of the four forces of nature, is responsible for binding together the protons and neutrons, collectively hadrons, that occur throughout the Universe. This dissertation seeks to characterize the transition in the QCD phase diagram through both theoretical models and first principle methods, thereby leading to an increased understanding of the fundamental strong interaction. The QCD phase diagram, the primary object of study, is intimately related to the early Universe and the mechanism through which it evolved to the current state that we observe today. Namely, this study seeks to understand the transition that happened just after the Big Bang when protons and neutrons were created from their constituent quarks and gluons by mapping out the phase diagram of strongly-interacting matter. In this dissertation, I will describe the various Equations of State for QCD that I have developed along with my efforts to characterize the low-density transition region of the QCD phase diagram. The Equation of State is a crucial input for the simulations of strongly-interacting matter produced in the laboratory during heavy-ion collisions (HICs). Furthermore, the transition between dense, deconfined quark-gluon matter and hadronic matter is investigated through the study of the chemical freeze-out stage in HICs. By understanding the medium produced in these collisions, we study the primordial liquid of the Universe, the Quark-Gluon Plasma, and as a result, the mechanism by which quarks and gluons combine to form hadrons. These results are not only impactful for studies of the early Universe through heavy-ion-collision physics, but they are also important for the astrophysics community for studies of neutron-star mergers that also traverse paths across the QCD phase diagram in the low temperature, high density regime.Physics, Department o