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), 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), to appear in Annales de l’Institut Fourier.

Scarring of quasimodes on hyperbolic manifolds (with Lior Silberman), to appear in Nonlinearity.

$L^p$ norms of fractal restrictions of eigenfunctions on surfaces (with Malabika Pramanik), preprint.

On the number of points tangent to nodal sets of spherical harmonics (with Igor Wigman), preprint.

Sup-bound improvements on compact hyperbolic surfaces, in preparation.

Lower bounds on the $L^2$ closed horocycle restrictions of Eisenstein series on the modular surface (with Junehyuk Jung), in preparation.

Restricted entropy of eigenfunctions on manifolds with Anosov flows, in preparation.

 

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