This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $225,000 in funding to the University of California, San Diego from September 1, 2022 to August 31, 2025.
The award supports research advancing the basic understanding of outliers in the spectra of random networks, which can be used to deduce various network properties and have applications in machine learning, bioinformatics, and coding theory. The principal investigator will study general network models with certain symmetry properties, including homogeneous and inhomogeneous bipartite random graphs, uniform and non-uniform hypergraphs, and the hypergraph stochastic block model. The research employs techniques from combinatorics, probability, linear algebra, and statistics to analyze a randomized generalized eigenvalue algorithm and find thresholds for outlier existence in various graph and hypergraph models. An education component provides research training for graduate and undergraduate students. The award is part of the NSF's Mathematical and Physical Sciences program (CFDA 47.049), which supports increasing scientific knowledge and understanding of major problems through mathematical and physical sciences research.
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