MAGNETIC FIELDS AND SELF-GRAVITY ARE LIKELY TO PLAY IMPORTANT AND INTERCONNECTED ROLES IN THE EVOLUTION OF PROTOSTELLAR DISKS AROUND NEWLY FORMED STARS. WE PROPOSE TO USE A COMBINATION OF NUMERICAL SIMULATIONS AND ANALYTIC MODELS TO UNDERSTAND HOW NET MAGNETIC FIELDS EVOLVE DURING A SELF-GRAVITATING DISK PHASE AND WHETHER CONDITIONS IN SUCH DISKS ALLOW FOR THE COLLISIONAL GROWTH OF ICY PARTICLES AS A PRE-REQUISITE FOR EARLY PLANET FORMATION. WE WILL SPECIFICALLY SEEK TO ANSWER THREE MAIN QUESTIONS: (1) HOW DO SELF-GRAVITATING PROTOSTELLAR DISKS THREADED BY NET MAGNETIC FIELDS EVOLVE? TO ADDRESS THIS QUESTION WE WILL DEVELOP SIMULATIONS THAT INCLUDE SELF-GRAVITY AND EITHER IDEAL MAGNETOHYDRODYNAMICS (MHD) OR NON-IDEAL MHD INCLUDING AMBIPOLAR DIFFUSION. WE WILL QUANTIFY THE EFFECT OF NET FIELDS ON ANGULAR MOMENTUM TRANSPORT IN SELF-GRAVITATING DISKS AND DEVELOP A PHYSICAL UNDERSTANDING OF NET FLUX TRANSPORT THAT CAN BE USED IN LONG-TERM EVOLUTIONARY MODELS. (2) HOW DOES THE NET FLUX OF PROTOSTELLAR DISKS EVOLVE OVER LONG TIME SCALES? WE WILL DEVELOP SIMPLIFIED NUMERICAL MODELS THAT BUILD ON PRIOR WORK BY LUBOW PAPALOIZOU&PRINGLE (1994) AND GUILET&OGILVIE (2014). (3) HOW IS ENERGY DISSIPATED IN SELF-GRAVITATING DISKS? WE WILL USE IDEALIZED NUMERICAL EXPERIMENTS TO QUANTIFY THE BALANCE BETWEEN DISSIPATION IN LARGE-SCALE SPIRAL STRUCTURES VERSUS SMALL-SCALE TURBULENCE. WE WILL USE THE RESULTS TO BETTER UNDERSTAND WHETHER CONDITIONS IN EARLY PROTOSTELLAR DISKS ALLOW FOR THE INITIAL GROWTH OF ICY SOLID PARTICLES TO LARGER SIZES. THE PROPOSED STUDY IS A THEORETICAL INVESTIGATION INTO HOW BASIC PHYSICAL PROCESSES - DISK SELF-GRAVITY AND MAGNETIC FLUX TRANSPORT - AFFECT THE EVOLUTION OF PROTOSTELLAR DISKS DURING THE FORMATION OF STARS AND PLANETARY SYSTEMS. THE EXPECTED RESULTS ARE RELEVANT TO THE DIRECT IMAGING OF DISK STRUCTURE WITH SPACE ASTROPHYSICS MISSIONS AND TO THE INTERPRETATION OF EXOPLANET POPULATIONS VIA THEORETICAL MODELS THAT START WITH THE COLLISIONAL GROWTH OF SMALL PARTICLES.