My research interests are at the intersections of microlocal analysis, spectral theory, geometric measure theory, harmonic analysis, and probability.
Publications and preprints:
Fourier integral operators, fractal sets, and the regular value theorem (with Alex Iosevich and Krystal Taylor), Advances in Mathematics 228, (4), 2385-2402 (2011).
Average pointwise bounds for deformations of Schrodinger eigenfunctions (with John Toth), Annales Henri Poincare 14, (3), 611-637 (2012).
Intersections of sets, diophantine equations, and Fourier analysis (with Alex Iosevich and Krystal Taylor), Journal d’Analyse Mathematique 128 (1), 159-178 (2016).
Perturbations of the semiclassical Schrodinger equation on negatively curved surfaces (with Gabriel Rivière), Journal of the Institute of Mathematics of Jussieu 16, 787-835 (2017).
Restrictions of eigenfunctions to Cantor-type sets on manifolds (with Malabika Pramanik), to appear in International Mathematics Research Notices (2019).
Direction distribution for nodal components of random band-limited functions on surfaces (with Igor Wigman), to appear in Transactions of the American Mathematical Society (2020).
Effective bounds for monochromatic connectivity measures in two dimensions (with Matthew de Courcy-Ireland), submitted (2020).