The National Science Foundation (NSF) awarded a $200,000 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to Virginia Polytechnic Institute & State University (Virginia Tech) to fund research on disordered quantum matter. The three-year grant, active from August 1, 2023 to July 31, 2026, will support Virginia Tech's work to develop an underlying mathematical theory to better understand the properties of materials that could play a crucial role in creating quantum computers robust to defects and noise. The project aims to make substantial progress in understanding the time evolution and transport properties of disordered many-body quantum systems, with a focus on the many-body localization phenomenon and its stability under perturbations. This research is expected to advance the scientific community's understanding of theoretical physics and applied mathematics models, while also providing hands-on training opportunities for students involved in the project.