This spring I am teaching Math 510 Vector Calculus.
Iterative reconstruction of the wavespeed for the wave equation with bounded frequency boundary data,
with Maarten V. de Hoop. Inverse Problems. Vol. 32, No. 2, 025008, 21 pp., 2016.
Resonances and lower resolvent bounds,
with Semyon Dyatlov and Maciej Zworski. Journal of Spectral Theory. Vol. 5, No. 3, pp. 599–615, 2015.
Quantitative limiting absorption principle in the semiclassical limit. Geometric and Functional Analysis. Vol. 24, No. 3, pp. 740–747, 2014.
Nontrapping surfaces of revolution with long living resonances, with Daniel Kang and Andre Kessler. Mathematical Research Letters. Vol. 22, No. 1, pp. 23–42, 2015.
Approximation and equidistribution of phase shifts: spherical symmetry, with Jesse Gell-Redman, Andrew Hassell, and Peter Humphries. Communications in Mathematical Physics. Vol. 326, No. 1, pp. 209–236, 2014.
Resonance free regions for nontrapping manifolds with cusps. To appear in Analysis and PDE.
Sharp polynomial bounds on the number of Pollicott-Ruelle resonances,
with Semyon Dyatlov and Maciej Zworski. Ergodic Theory and Dynamical Systems. Vol. 34, No. 4, pp. 1168–1183, 2014.
Fractal Weyl laws for asymptotically hyperbolic manifolds,
with Semyon Dyatlov. Geometric and Functional Analysis. Vol. 23, No. 4, pp. 1145–1206, 2013.
Semiclassical resolvent estimates at trapped sets,
with András Vasy. Annales de l'Institut Fourier, Vol. 62, No. 6, pp. 2379–2384, 2012.
Inverse problems in spectral geometry,
with Hamid Hezari. Inverse Problems and Applications: Inside Out II. Mathematical Sciences Research Institute Publications, No. 60, pp. 455–486, 2012.
Extending cutoff resolvent estimates via propagation of singularities. Communications in Partial Differential Equations, Vol. 37, No. 8, pp. 1456–1461, 2012.
Resonant uniqueness of radial semiclassical Schrödinger operators,
with Hamid Hezari. Applied Mathematics Research Express, Vol. 2012, No. 1, pp. 105–113, 2012.
Spectral uniqueness of radial semiclassical Schrödinger operators,
with Hamid Hezari and Ivan Ventura. Mathematical Research Letters, Vol. 18, No. 3, pp. 521–529, 2011.
Propagation through trapped sets and semiclassical resolvent estimates,
with András Vasy. Annales de l'Institut Fourier, Vol. 62, No. 6, pp. 2347–2377, 2012. See also a short report on the result.
Gluing semiclassical resolvent estimates via propagation of singularities,
with András Vasy. International Mathematics Research Notices, Vol. 2012, No. 23, pp. 5409–5443, 2012. See also my coauthor's short report on the result.
Solitary waves for the Hartree equation with a slowly varying potential,
with Ivan Ventura. Pacific Journal of Mathematics, Vol. 248, No. 1, pp. 63–90, 2010.
Fast soliton scattering by attractive delta impurities, with
Communications in Partial Differential Equations, Vol. 34, No. 9, pp. 1074–1113, 2009.
Local smoothing for scattering manifolds with hyperbolic trapped sets.
Communications in Mathematical Physics, Vol. 286, No. 3, pp. 837–850, 2009.
Introduction to the method of complex scaling, 2006.
A Midwestern Microlocal Meeting took place on May 16th and 17th, 2015, at Northwestern University.
Math 366 Ordinary Differential Equations.
Math 266 Ordinary Differential Equations.
Math 265 Linear Algebra.
18.104 Seminar in Analysis: Distribution Theory.
18.100B Real Analysis.