As astronomers observe more and more dusty proto-stellar disks, a fuller understanding of the process of planetary formation becomes possible. This work is to explore an entirely new method of determining structures in proto-planetary disks. The team will map out concentrations of carbon and oxygen isotopes using spectroscopic imaging of CO isotopologues. The team will conduct a spectroscopic study of existing ALMA observations as well as new observations to be made by the team. They will examine structures such as spirals, gaps and rings. They will also determine the gas composition of young proto-stellar disks, the evolution of composition through different phases of disk evolution and determine the mass of the central protostar. The results of this work will provide new observational constraints for models of planetary formation. Two PhD theses will be completed under this program, both by students from under-represented groups. This program will also support Hawaiian native undergraduate students for summer research work both in analysis and in hardware development. Outreach activities include public talks and summer camp programs for high-school students.<br/><br/>The team will use a self-developed state-of-the-art modeling code called Protoplanetary Disks and Stars with Python (pdspy) to extract structural information about protoplanetary disks from multispectral ALMA imaging. The pdspy code models multi-wavelength observational datasets, particularly ALMA images like those to be obtained through the team’s ALMA Large Program, with full radiative transfer models of physically motivated Keplerian disk + rotating collapsing envelope systems using Bayesian parameter estimation methods such as Markov Chain Monte Carlo or Nested Sampling to rigorously sample parameter space. The team will observe and study protoplanetary disks at different points in disk formation and evolution, from initial formation into the T Tauri phase of protostellar development.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.