Assistant Professor
Department of Mathematics
Purdue University
150 North University Street
West Lafayette, IN 479072067
Office: 602 Mathematical Sciences Building
Teaching
In Fall 2018 I am teaching
MA 341 Foundations of Analysis.
Papers

Wave asymptotics for manifolds with infinite cylindrical ends,
with Tanya Christiansen.

Resolvent estimates on asymptotically cylindrical manifolds and on the half line,
with Tanya Christiansen.
 Exponential lower resolvent bounds far away from trapped sets,
with Long Jin. To appear in Journal of Spectral Theory.
 Resonance free regions for nontrapping manifolds with cusps. Analysis and PDE. Vol. 9, No. 4, pp. 907–953, 2016.
 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.
 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.
 Quantitative limiting absorption principle in the semiclassical limit. Geometric and Functional Analysis. Vol. 24, No. 3, pp. 740–747, 2014.
 Sharp polynomial bounds on the number of PollicottRuelle resonances,
with Semyon Dyatlov and Maciej Zworski. Ergodic Theory and Dynamical Systems. Vol. 34, No. 4, pp. 1168–1183, 2014.
 Approximation and equidistribution of phase shifts: spherical symmetry, with Jesse GellRedman, Andrew Hassell, and Peter Humphries. Communications in Mathematical Physics. Vol. 326, No. 1, pp. 209–236, 2014.
 Fractal Weyl laws for asymptotically hyperbolic manifolds,
with Semyon Dyatlov. Geometric and Functional Analysis. Vol. 23, No. 4, pp. 1145–1206, 2013.
 Extending cutoff resolvent estimates via propagation of singularities. Communications in Partial Differential Equations, Vol. 37, No. 8, pp. 1456–1461, 2012.
 Semiclassical resolvent estimates at trapped sets,
with András Vasy. Annales de l'Institut Fourier, Vol. 62, No. 6, pp. 2379–2384, 2012.
 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.

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.
 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.
 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
Justin Holmer.
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.
Former PhD Student
I have supervised one PhD student,
Jacob Shapiro, who graduated in 2018.
Conferences
I have coorganized two May Midwestern Microlocal Meetings. The
first took place at Northwestern in 2015 and the
second took place at Purdue in 2017.
Previous Teaching