I am an Assistant Professor at the Department of Mathematics and Statistics at James Madison University .
Before that, I was a postdoc at the University of Michigan- Ann Arbor mathematics department .
I finished my Ph.D. at the
Courant Institute of Mathematical Sciences at
New York University in Sept 2010, under the supervision of Professor
Robert V. Kohn.
Mathematical Modeling in Materials Science
I use methods from PDE, dynamical systems, and numerical analysis to study
higher order evolution equations,
gradient flow partial differential equations,
self-similarity in the solutions of nonlinear partial differential equations,
stability analysis for critical points of non-linear flows,
PDE and discrete step models for epitaxial structures.
Inverse Problems and Imaging
Inverse problems in threat detection: I have studied uniqueness related to inverting the advection-diffusion equation.
I also worked on numerical L^1-minimization methods.
Inverse scattering theory: A typical application is the imaging of the subsurface.
My focus is on the inversion of a hybrid-type Bremmer series, to determine the scattering potential of a bounded medium from boundary measurements of a scattered wave.
Gibran.. On Children and On Love
Department of Mathematics and Statistics
305 Roop Hall MSC
James Madison University
Harrisonburg, VA 22807
Office location: 118 Roop Hall
Office Phone: (540) 568-3807