My research interests are in microlocal analysis and partial differential equations. I am currently working on projects in spectral theory, geometric measure theory, and dynamical systems.
Here is my curriculum vitae
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), accepted (with minor revisions) to International Mathematics Research Notices.
Intersections of sets, diophantine equations, and Fourier analysis (with Alex Iosevich and Krystal Taylor), to appear in Journal d'Analyse Mathematique (2014).
Perturbations of the semiclassical Schrodinger equation on negatively curved surfaces (with Gabriel Riviere), submitted.
Strong scarring and closed hyperbolic trajectories (with Stephane Nonnenmacher), preprint available upon request.
Summer 2012: MATH 315
Summer 2013: MATH 262
Summer 2015: MATH 222