Research

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), publish online in International Mathematics Research Notices (2015),  doi: 10.1093/imrn/rnv256.

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 periods, published online in Journal of Geometric Analysis (2015), doi: 10.1007/s12220-014-9554-6.

Perturbations of the semiclassical Schrodinger equation on negatively curved surfaces (with Gabriel Rivière), to appear in Journal of the Institute of Mathematics of Jussieu (2015), doi:10.1017/S1474748015000262.

Strong scarring of logarithmic quasimodes (with Stéphane Nonnenmacher), to appear in Annales de l’Institut Fourier.

Scarring of quasimodes on hyperbolic manifolds (with Lior Silberman), submitted