- The direct scattering problem of the Intermediate Long Wave equation

(with Peter Perry).**Abstract**: This is a project to explore the complete integrability of the Intermediate Long Wave (ILW) Equation, which is a model of internal gravity waves in a two layer fluid. The ILW equation is an equation to bridge between the Kortweg-deVries equation and the Benjamin-Ono equation. - The Inverse scattering problem of the Benjamin-Ono equation

**Abstract**: This is a project to study the large data inverse scattering problem of the Benjamin-Ono equation. This will rigorously establish the complete integrability in a more general setting than is currently available in the literature. - The stability of disc galaxies

(with Walter Strauss).**Abstract**: This is a project to study fluid and kinetic models of 2D galaxies. Existence and stability of rotating solutions are explored. - Global continuation of surface waves on a 2D droplet

(with Gary Moon).**Abstract**: This is a project to construct steady surface capillary waves on a 2D droplet of water. Local and global continuation results will be proven.

- Global Continuation of a Vlasov Model of Rotating Galaxies

(with Walter Strauss), accepted by*Kinetic and Related Models*. - Existence of Rotating Stars with Variable Entropy

(with Juhi Jang and Walter Strauss), accepted by*SIAM Journal of Mathematical Analysis*. - Rapidly Rotating White Dwarfs

(with Walter Strauss),*Nonlinearity*, 33.9 (2020): 4783. - Global Continuation and the Theory of Rotating Stars

*Quarterly of Applied Mathematics*, 78.1 (2020): 147-159. - Rapidly Rotating Stars

(with Walter Strauss),*Communications in Mathematical Physics*, 368 (2020): 701-721. - Existence of Rotating Magnetic Stars

(with Juhi Jang and Walter Strauss),*Phyisica D: Nonlinear Phenomena*397 (2019): 65-74. - Steady States of Rotating Stars and Galaxies

(with Walter Strauss),*SIAM Journal on Mathematical Analysis*49.6 (2017): 4865-4914. - Jost Solutions and the Direct Scattering Problem of the Benjamin-Ono Equation

*SIAM Journal on Mathematical Analysis*49.6 (2017): 5158-5206. - Simplicity and Finiteness of Discrete Spectrum of the Benjamin-Ono Scattering
Operator

*SIAM Journal on Mathematical Analysis*48.2 (2016): 1348-1367. - Existence of rotating planet solutions to the Euler-Poisson equations with an inner
hard core

*Archive for Rational Mechanics and Analysis*219 (2016): 1-26. - On rotating star solutions to the non-isentropic Euler-Poisson equations

*Journal of Differential Equations*259.12 (2015): 7161-7198.