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 (updated 10/14/14).
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), submitted.
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.
Logarithmic quasimodes and variable negative curvature (with Stephane Nonnenmacher), in preparation.
Summer 2012: MATH 315
Winter 2013: I did not teach this semester.
Summer 2013: MATH 262