Faculty

Research Overview

Research Interests

• Partial differential equations; Mathematical physics

Courses Taught

• MTH 190:  Topics in Problem Solving
• MATH 471:  Real Analysis

Selected Publications

Preprints

• Sharp global regularity for the 2+1-dimensional equivariant Faddeev model (with Kenji Nakanishi and Xiang Zhang), Int. Math. Res. Not. 2015 (2015), rnv037-17.
• Ill-posedness results for generalized Boussinesq equations (with A. Alexandrou Himonas and David Karapetyan), Nonlinear Anal. 95 (2014), 404-413.
• Restricted convolution inequalities, multilinear operators and applications (with Allan Greenleaf, Alex Iosevich, Eyvindur Palsson, and Eric Sawyer), Math. Res. Lett. 20 (2013), 675-694.
• On the regularity of the 2+1-dimensional equivariant Skyrme model (with Daniel da Silva), Proc. Amer. Math. Soc. 141 (2013), 2105-2115.
• Global well-posedness and scattering for Skyrme wave maps (with Kenji Nakanishi and Sarada Rajeev), Commun. Pure Appl. Anal. 11 (2012), 1923-1933.
• Nonconcentration of energy for a semilinear Skyrme model (with Sarada Rajeev), Ann. Physics 325 (2010), 2697-2706.
• A continuity argument for a semilinear Skyrme model (with Sarada Rajeev), Electron. J. Differential Equations 2010 (2010), No. 86, 1-9.
• A remark on an equation of wave maps type with variable coefficients, Math. Res. Lett. 16 (2009), 395-404.
• A phase space transform adapted to the wave equation (with Daniel Tataru), Comm. Partial Differential Equations 32 (2007), 1065-1101.