Dark matter aggregates under its own gravity to form tightly bound clumps called dark matter ?halos?. As these halos form, they pull atoms of regular matter into them, enabling the formation of the stars and galaxies we see today. For this reason, dark matter halos are the foundational building blocks for our understanding of how galaxies are distributed in the Universe. Over the past few years, a variety of works have demonstrated that our definitions of dark matter halos do not adequately capture their inner structure, compromising our ability to use a halo-based description of the Universe when interpreting astronomical survey data. A collaboration between scientists at the University of Arizona and the University of Maryland propose to address this deficiency by providing the first fully physically motivated definition of dark matter halos. Based on this, the team will then develop an accurate theoretical model for interpreting data from large galaxy surveys. The Principal Investigator at the University of Arizona will be an active participant in the Tucson Initiative for Minority Engagement in STEM Program, organizing workshops, seminars, and coordinating mentoring activities in the program. The Principal Investigator at the University of Maryland will develop a user-friendly web-interface for the code Colossus to allow for simple visualizations that can be adopted for use in introductory and non-major astronomy courses. This project proposes a radical redefinition of dark matter halos that will enable the construction of percent-level accurate halo models of large-scale structure. The model is built on the inherent dichotomy between particles orbiting a halo and those falling into the halo for the first time. The proposing team has demonstrated that the orbiting and infalling contributions to halo correlation functions roughly correspond to the one- and two-halo terms of the traditional halo model. However, the orbiting/infalling halo model framework is both mathematically simpler and significantly more accurate than the traditional halo model approach. The team will develop the proposed physical halo model framework based on the orbiting/infalling dichotomy. They will then construct halo catalogs based on this revised halo definition for a broad range of simulated cosmologies and redshifts, and use the resulting halo catalogs to calibrate the halo mass function, bias function, and various halo correlation functions. The code and halo catalogs produced by this work will be made publicly available. 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.