Research

My research interests are at the intersections of microlocal analysis, spectral theory, geometric measure theory, harmonic analysis, and probability.

Publications and preprints:

Microlocal analysis of scattering data for nested conormal potentials, Ph.D. thesis, Journal of Functional Analysis 262 (5), 2100-2141 (2012).

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).

Smooth billiards with a large Weyl remainder (with Iosif Polterovich and John Toth), International Mathematics Research Notices 12, 3639-3677 (2016).

Intersections of sets, diophantine equations, and Fourier analysis (with Alex Iosevich and Krystal Taylor), Journal d’Analyse Mathematique 128 (1), 159-178 (2016).

Expected values of eigenfunction periodsJournal of Geometric Analysis  26, 360-377 (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).

Strong scarring of logarithmic quasimodes (with Stéphane Nonnenmacher), Annales de l’Institut Fourier, Volume 67 (6), 2307-2347 (2107).

Scarring of quasimodes on hyperbolic manifolds (with Lior Silberman), Nonlinearity, Volume 31, Issue 1 (2018).

Tangent nodal sets for random spherical harmonics, CRM Proceedings and Lecture Notes Series: Probabilistic Methods in Geometry, Topology and Spectral Theory (2018).

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).