This Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support a collaborative research project between Carnegie Mellon University (CMU) researchers in mathematics and computer science. The $418,035 award, effective October 1, 2024, will explore new ways to address complex mathematical problems by integrating advanced machine learning techniques with automated reasoning. The research team will use three specific open problems within graph theory and combinatorics as test cases to evaluate the effectiveness of new algorithms. Key objectives include applying machine learning to develop efficient symmetry-breaking clauses, using transformer-based methods to generate small Folkman graphs, and tackling a realizability problem related to point sets in a plane. This cross-disciplinary effort aims to advance the knowledge of long-standing open problems in mathematics and computer science, with potential applications in ensuring software reliability, security, and efficiency. The award will support the work of two student researchers, a mathematician and a computer scientist, who will closely collaborate to achieve the project's goals.
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