If the Fourier transform of a function is zero everywhere except within a thin neighborhood of a submanifold of Euclidean space, what can we say about the function itself? This question is at the heart of Fourier restriction theory, and it motivates many problems in modern Fourier analysis and its applications in number theory, geometric measure theory, and combinatorics. I am especially interested in what we can say about the shape of the level sets of such a function.
Tangency counting for well-spaced circles (2025). Written with Dominique Maldague.
A sharp weighted Fourier extension estimate for the cone in R^3 based on circle tangencies (2024).
Description of the code ANVIL (ANisotropic Vhf Impulse Location). Radio Science (2018). Written with Heidi Morris.
Expository article: "Bounded orthogonal systems and the Lambda(p)-set problem" by Jean Bourgain. Expositiones Mathematicae (2025). Written with Hongki Jung, Bartosz Langowski, and Truong Vu.Â
A Study Guide to "Kaufman and Falconer estimates for radial projections" (2023). Written with Paige Bright, Caleb Marshall, and Ryan Bushling.
Notes on Bourgain's paper "Besicovitch-type maximal operators and applications to Fourier analysis". Written with Ben Foster and Itamar Oliveira