Non-concentration is a theme in problems from Fourier analysis, incidence geometry, and analytic number theory. I am fascinated by the interplay of curvature and problems involving non-concentration. My recent work explores continuum analogs of classical theorems from geometry, namely circle tangencies and Beck's theorem.
A Continuum Beck-type Theorem for Hyperplanes (2025). Written with Paige Bright and Dmitrii Zakharov.
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), to appear in Journal d'Analyse Mathématique.
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.
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