Support: National Science Foundation (NSF)

Period of Performance: August, 1st, 2023 – July 31st, 2026

Budget: $146,000

Summary: This project studies mathematical properties of a specific class of non-local operators which arise in data science problems. In particular, this project studies 1) non-local perimeter problems arising from adversarial machine learning, and 2) non-local Dirichlet problems arising from unsupervised and semi-supervised classification problems. The goal will be to establish detailed smoothness estimates on solutions to these problems by developing novel analytical tools. These results will provide an improved foundation for contemporary algorithms, and may eventually lead to improvements of the same.