This $150,000 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences (CFDA 47.049 - Mathematical and Physical Sciences) supports research led by San Jose State University Research Foundation on the connections between the geometric and arithmetic structure of fractal sets and their Fourier transforms.
The overarching objectives are to solve problems in constructing fractal Salem sets, calculating the Fourier dimension of fractals, and optimizing Fourier restrictions on fractal sets. This work will be conducted in collaboration with undergraduate and graduate students, aligning with the grant's goal of training future mathematicians and STEM professionals. The findings are expected to provide insights that will benefit research in areas like geometric measure theory, additive combinatorics, and partial differential equations. The award period is from Sep 1, 2024 to Aug 31, 2027.