Searching for the Quantum Chromodynamic Critical Point

Under extreme temperature and density conditions, the quarks and gluons that are normally confined to nucleons are able to move freely in a state known as the quark-gluon plasma (QGP). Currently, droplets of QGP can be created experimentally using heavy-ion collisions at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory and at the Large Hadron Collider (LHC) at CERN. It is known from first principle quantum chromodynamics (QCD) calculations that the transition from nuclear matter to the QGP is a crossover if the system has a net baryon density of zero, which has been consistent with experimental results. One of the key questions in the field is whether QCD exhibits a first-order phase transition at large baryon densities. In this scenario, a critical point would mark the end of the crossover phase transition and the beginning of the first order line. In this thesis, I detail my study of the implications of the presence of a critical point on the QCD phase diagram. In the first part of this work, I construct a family of equations of state matching lattice calculations at low baryon density, and including a critical point in the correct universality class. I then employ the equation of state I developed in the analysis of a possible critical point signature that can be detected experimentally at RHIC. I also use a Feed-Forward Neural Network to identify critical point configurations that result in inconsistent thermodynamics.