This $443,217 Project Grant award from the National Science Foundation's (NSF) Computer and Information Science and Engineering (CISE) program (CFDA 47.070) supports research on fast combinatorial algorithms for graph problems such as maximum matching, maximum flow, and shortest paths. The award aims to develop new algorithms for dynamic graphs, where the graph structure changes over time, as well as improve expander-related tools that can serve as building blocks for many graph algorithms. The research, led by the Toyota Technological Institute at Chicago (TTIC), a private non-profit university, focuses on advancing the theoretical foundations of graph algorithms with the goal of improving computational efficiency and performance. As a sub-awardee, TTIC has also contributed to projects on machine learning efficiency and robustness, working with partners like the University of Wisconsin-Madison. The award will fund this research over the period from July 1, 2024 to June 30, 2028.