Interests
My main mathematical interests are in applications of harmonic analysis to
partial differential equations and mathematical physics.
I am particularly interested in oscillatory and singular integrals and integral operators
that arise in the analysis of dispersive PDEs such as the Schrödinger, wave and Dirac equations.
Starting September 2017 my work will be supported by the Simons Foundation under grant #511825.
Links
Google Scholar Profile
MathSciNet (Subscription Required)
arXiv
Publications
 (with M.B. Erdogan)
"Dispersive estimates for the Schrödinger equation for
C$^{\frac{n3}{2}}$ potentials in odd dimensions,"
International Mathematics
Research Notices
2010:13, 25322565.
[preprint], [Journal
Version]

"Dispersive estimates for the matrix and scalar Schrödinger equation in
dimension five," Illinois J. Math. Volume 56, Number 2 (2012), 307341.
[preprint],
[Journal Version].

"Abel's theorem simplifies reduction of order."
College Mathematics Journal,
Vol. 42, No. 5, November 2011 , pp. 399402(4).
[preprint], [Journal
Version].

"Using Abel's theorem to explain repeated roots
of the characteristic equation." CODEE Journal, July 2011.
URL http://www.codee.org/ref/CJ110679.
 (with M.B. Erdogan)
"Dispersive estimates for twodimensional Schrödinger operators with
obstructions at zero energy."
Trans. Amer. Math. Soc. 365 (2013), 64036440.
[preprint], [Journal Version].

(with H.I. Dwyer)
"Integrating factors and repeated roots of the characteristic equation."
CODEE Journal, January 2012. URL http://www.codee.org/ref/CJ120930.

(with M.B. Erdogan)
"A weighted dispersive estimate for Schrödinger
operators in dimension two."
Comm. Math. Phys. 319 (2013), 791811.
[preprint]. [Journal Version].

(with M.B. Erdogan)
"Dispersive estimates for matrix Schrödinger
operators in dimension two."
DCDSA. Pages: 4473  4495, Volume 33, Issue 10, October 2013.
[preprint]. [Journal Version].

(with Dirk
Hundertmark)
"Exponential decay for dispersion managed solitons for general dispersion profiles,"
Letters in Mathematical Physics, Volume 106, Issue 2, 221249.
[preprint]. [Journal Version].

"Time decay estimates for the wave equation with potential in dimension two,"
Journal of Differential Equations 257 (2014)
pp. 868919.
[preprint],
[Journal Version]

(with M.B. Erdogan and
M.J. Goldberg)
"Dispersive estimates for four dimensional Schrödinger
and wave equations with obstructions at zero energy." Comm. PDE 39 (2014),
no. 10, 19361964.
[preprint],
[Journal Version]

(with M.J. Goldberg)
"Dispersive Estimates for higher
dimensional Schrödinger Operators with threshold
eigenvalues I: The odd dimensional case,"
J. Funct. Anal. 269 (2015) no. 3, 633682. [preprint],
[Journal Version]

(with M.J. Goldberg)
"Dispersive Estimates for higher
dimensional Schrödinger Operators with threshold
eigenvalues II: The even dimensional case," J. Spectr. Theory 7 (2017), 3386. [preprint], [Journal Version].

(with M.J. Goldberg)
"The $L^p$ boundedness of wave operators for higher
dimensional Schrödinger Operators with threshold
singularities," Advances in Mathematics, 303 (2016), 360389.
[preprint], [Journal Version]

(with E. Toprak)
"Decay estimates for four dimensional Schrödinger, KleinGordon and wave equations with
obstructions at zero energy." Differential and Integral Equations, Volume 30, Number 5/6 (2017), 329386.
[preprint], [Journal Version].

(with M.B. Erdogan)
"The Dirac equation in two dimensions: Dispersive estimates and classification of threshold obstructions."
Comm. Math. Phys. 352 (2017), no. 2, 719757.
[preprint], [Journal Version]

(with M.J. Goldberg)
"On the $L^p$ boundedness for fourdimensional wave operators for Schrödinger Operators with a threshold
eigenvalue," Ann. Henri Poincaré 18 (2017),
no.4, 12691288. [preprint], [Journal Version]
, [Free Journal Version].

(with M.B. Erdogan and E. Toprak)
"Dispersive estimates for Dirac Operators in dimension three with
obstructions at threshold energies"
[preprint], submitted, 36 pp.

(with M.B. Erdogan and M.J. Goldberg)
"On the $L^p$ boundedness of wave operators for twodimensional Schrödinger Operators with threshold
obstructions," [preprint], submitted, 21pp.

(with M.B. Erdogan and M.J. Goldberg)
"Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions," [preprint], submitted, 26 pp.

(with M.B. Erdogan and E. Toprak)
"Dispersive estimates for massive Dirac operators in dimension two"
[preprint], submitted, 40 pp.
William Green's Homepage