Current Projects:  

General Relativistic Dirac operators and their spectrum 

Dispersive estimates for singular potentials 

Publications: 

• (with M. Xie) " Global solutions for 5-D Quadratic Fourth Order Schrödinger equation" [pdf]  

• (with A. Black, B. Vergara and J. Zhou) "Pointwise decay for radial solutions of the Schrödinger equation with a repulsive Coulomb potential " [pdf] 

•  "Bounds on the number of scattering poles of half-Laplacian in odd dimensions d\geq 3." [pdf] (submitted)

•  (with  M. K.-H. Kiessling, A. S. Tahvildar-Zadeh) "Essential Self-Adjointness of Dirac operators under the influence of general-relativistic gravity." 16th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories, 2023

• (with B. Erdoğan and W.Green ) " "What is the Dirac equation?", Notices Amer. Math. Soc. 68 (2021), no. 10, 1782--1785. 

• (with  M. K.-H. Kiessling, A. S. Tahvildar-Zadeh) "On the Dirac operator for a test electron in a Reissner--Weyl--Nordstrom black hole spacetime",  General Relativity and Gravitation (2021),  53 (1) -[pdf]

• (with B. Erdoğan and W.Green ) "On the Fourth order Schrodinger equation in three dimensions: dispersive estimates and zero energy resonances ",  J. Differential Equations (2021), Volume 271, 152-185 - [pdf],

• (with  M. K.-H. Kiessling, A. S. Tahvildar-Zadeh) "On General- Relativistic Hydrogen and Hydrogenic Ions",  J. Math. Physcs (2020) 61, 092303 - appeared as Editor's pick. [pdf]

• (with W.Green ) "On the Fourth order Schrodinger equation in four dimensions: dispersive estimates and zero energy resonances, J. Differential Equations (2019), Volume 267, 1899-1954, [pdf]

• (with B. Erdoğan and W.Green ) "Dispersive estimates for massive Dirac operators in dimension two ",J. Differential Equations (2018), Volume 264, 5802-5837 [pdf]

• (with B. Erdoğan and W.Green ) "Dispersive estimates for Dirac operators in dimension three with obstructions at threshold energies ", Amer. J. Math., Volume 141, No 5, October 2019, pp.1217-1258 [pdf]

• (with W.Green ) "Decay estimates for four dimensional Schrodinger, Klein Gordon and wave equations with obstructions at zero energy",Differential and Integral Equations, Volume 30, Number 5/6 (2017), 329-386 [pdf]

• A weighted estimate for two dimensional Schrodinger, Matrix Schrodinger and wave equations with resonance of the first kind at zero.", J. Spectr. Theory 7 (2017), 1235-1284. [pdf]