Are you a graduate student potentially interested in working with me? Please see this page for a brief description of my interests and advice on which qualifying exams to take.

I am an associate professor in the math department at Texas
A&M University. Before coming here, I was a Boas Assistant
Professor at Northwestern
University. I received my Ph.D. from Stanford University in 2010.
I was a student of Rafe
Mazzeo
and András
Vasy.

I am interested in partial differential equations generally and
geometric microlocal analysis more specifically. Here is my (current
as of August 20, 2019) CV. I am supported by NSF CAREER grant DMS-1654056.

**Papers**

- A parametrix for the forward fundamental
solution of the Klein-Gordon equation on asymptotically de Sitter
spaces.

Published in Journal of Functional Analysis 259:1673-1719 (2010).

Also available from the ArXiv. (Last updated: August 10, 2010) - A Strichartz estimate for de Sitter
space.

Published in the Proceedings of the Centre for Mathematics and its Applications ANU 44:97-104 (2010).

Also available from the ArXiv. (Last updated: July 28, 2011) - Strichartz estimates on asymptotically de
Sitter spaces.

Published in Annales Henri Poincaré 14(2):221--252 (2013).

Also available from the ArXiv. (Last updated: June 13, 2012) - Radiation fields for semilinear wave
equations. Joint with Antônio Sá Barreto.

Published in Transactions of the American Mathematical Society 367:3873--3900 (2015).

Also available from the ArXiv. (Last updated: December 19, 2012) - Resolvent estimates and local decay of
waves on conic manifolds. Joint with Jared Wunsch.

Published in Journal of Differential Geometry 95:183--214 (2013).

Also available from the ArXiv. (Last updated: October 1, 2012) - Equipartition of energy in geometric
scattering theory.

Published in Journal d'Analyse Mathematique 123:341--353 (2014).

Also available from the ArXiv. (Last updated: April 1, 2013) - Some global aspects of linear wave
equstions. Joint with Rafe Mazzeo.

Published in Evolution Equations, Clay Mathematics Proceedings, 17:73--96 (2013).

Also available from the ArXiv. (Last updated: November 14, 2012) - Strichartz estimates on
exterior polygonal domains. Joint with Jeremy Marzuola and
Jared Wunsch.

Published in Geometric and Spectral Analysis, Contemporary Mathematics, 630:291--306 (2014).

Also available from the ArXiv. (Last updated: April 19, 2013) - Asymptotics of radiation fields on
asymptotically Minkowski space. Joint with András Vasy
and Jared Wunsch.

Published in American Journal of Mathematics 137(5):1293--1364 (2015).

Also available from the ArXiv. (Last updated: June 26, 2014) - Radiation fields on Schwarzschild
spacetime. Joint with Fang Wang.

Published in Communications in Mathematical Physics 331:477--506 (2014).

Also available from the ArXiv. (Last updated: January 10, 2013) - Sharp high-frequency estimates for the
Helmholtz equation and applications to boundary integral
equations. Joint with Euan Spence and Jared Wunsch.

Published in SIAM Journal of Mathematical Analysis 48(1):229--267 (2016).

Also available from the ArXiv. (Last updated: October 16, 2015) -
Asymptotics of scalar waves on long-range
asymptotically Minkowski spaces. Joint with András Vasy
and Jared Wunsch.

Published in Advances in Mathematics 328:160--216 (2018).

Also available from the ArXiv. (Last updated: January 22, 2018) -
An explicit description of the radiation field
in 3+1-dimensions.

Published in "Spectral and scattering theory and related topics. Proceedings of a symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, January 20--22, 2016". Available from the ArXiv. (Last updated: February 2, 2017) -
Locating the resonances on hyperbolic
cones. Joint with Jeremy Marzuola.

Published in Mathematical Research Letters 26(2):365--381 (2019). Preprint, arXiv:1608.05278. Available from the ArXiv. (Last updated: March 26, 2018) -
Scattering resonances on truncated
cones. Joint with Mengxuan Yang.

Preprint, arXiv:1903.02654. Available from the ArXiv. (Last updated: March 6, 2019) -
The radiation field on product cones.
Joint with Jeremy Marzuola.

Preprint, arXiv:1906.04769. Available from the ArXiv. (Last updated: June 24, 2019) -
Riemann moduli spaces are quantum
ergodic. Joint with Jesse Gell-Redman and Xiaolong Han.

Preprint, arXiv:1908.06949. Available from the ArXiv. (Last updated: August 20, 2019)

**Seminars**

**Teaching**

- I am currently (Spring 2020) teaching two sections of Math 171.
- I am also currently facilitating the graduate student writing groups.
- In Fall 2018 I taught two honors sections of Math 151, the one-variable engineering calculus course.
- In Spring 2018 I facilitated the graduate student writing groups with Julia Plavnik. In Spring 2019 I did this again with Emanuele Ventura.
- In Fall 2017 I taught:
- In Spring 2017, I taught Math 622, a first graduate course in differential geometry.
- In Fall 2016, I taught Math 689, a graduate topics course on microlocal analysis.
- In Fall 2015, I taught Math 308 (a course on differential equations) and Math 460 (a course on general relativity).
- In Spring 2015, I taught Math 304, a course on linear algebra.
- In Fall 2014, I taught Math 221, a multivariable calculus course for science and math majors. The course was administered through eCampus (and so there is no accessible course website).
**Northwestern University**- In Autumn 2013 I taught Math 381: Fourier Series and Boundary Value Problems for ISP.
- I gave two lectures on the WKB approximation at theNorthwestern University undergraduate conference on "Quantization and Mathematics".
- In Winter 2012 I taught Math 360 MENU Applied Analysis. This is the second quarter of a two-quarter sequence and introduces students to ODEs with MATLAB. In Autumn 2011 I taught the first quarter of the sequence.
- In Autumn 2010 I taught Math 220 and in Winter 2011 I taught Math 224. These are the first and second quarters of single-variable calculus.

- At Stanford University, I was a teaching assistant for linear algebra and multivariable calculus, ordinary differential equations, and honors multivariable calculus. I was also the course assistant for graduate courses in functional analysis and harmonic analysis, and for advanced undergraduate courses in differential topology and Galois theory.

**Conference Organization**

- I was on the organizing committee (with Raphael Hora, Gerardo Mendoza, Wagner Muniz, and Antônio Sá Barreto) of the Third Symposium on Scattering and Spectral Theory, to be held July 17 to 28, 2017, in Florianópolis, Brazil.
- I helped organize the 56th meeting of the Texas Geometry and Topology Conference, held November 4--6, 2016 at Texas A&M University.
- I organized (with Luc Hillairet and Jared Wunsch) a workshop on "Evolution equations on singular spaces" at CIRM in Luminy, France, which was held April 25--29, 2016.
- I was an organizer (with Valentino Tosatti, Ben Weinkove, Jared Wunsch, and Steve Zelditch) of the 73rd Midwest PDE Seminar, held at Northwestern University during the weekend of May 10-11, 2014.
- I also organized (with Igor Rodnianski, Gigliola Staffilani, and Jared Wunsch) a workshop on evolution equations in honor of Terence Tao at Northwestern University in May 2012.
- I was an organizer (with Emmanuel Schenck, András Vasy, Jared Wunsch, and Steve Zelditch) of the Microlocal Methods In Spectral and Scattering Theory workshop at Northwestern University in October 2011.

**Collaborators**