NONTECHNICAL SUMMARY Superconductivity — the ability of certain materials to conduct electricity with zero resistance — was one of the landmark discoveries of twentieth-century physics. It revolutionized technology, enabling powerful magnets for particle accelerators and MRI machines, maglev trains, and today serves as a promising foundation for quantum computing. Superconductivity also deepened our understanding of nature by revealing a remarkable quantum state visible on macroscopic scales. Yet, even after decades of research, many superconductors defy conventional explanations. They appear and persist under conditions where standard theory predicts they should not exist, leaving the mechanisms behind them largely unknown. This project seeks to uncover how superconductivity emerges in these unconventional systems — specifically those with very low electron density and strong electron-electron repulsion, both normally hostile to superconductivity. By studying representative materials where unusual behavior is observed, the PI will identify plausible microscopic mechanisms, evaluate them against experimental data, and propose new measurements to distinguish between competing scenarios. This effort will clarify how exotic superconducting states form, what makes them unique, and how they might be engineered or controlled. Ultimately, the results will guide the search for new superconducting phases and advance their potential use in future technologies. The educational component aims to broaden participation in science and strengthen the future quantum workforce. The PI will expand undergraduate involvement in theoretical physics research and spark scientific interest among high-school students and educators in the Pittsburgh region. Outreach activities — conducted through the Sigma Xi honorary research society and in collaboration with Carnegie Mellon’s Eberly Center and Leonard Gelfand Center — will include public lectures, science fairs, teacher-facing work