- Partial Differential Equations
- Nonlocal and Fractional Models
- Variational Methods, Potential Theory
- Elliptic and Hyperbolic Equations
- Harmonic Analysis
- Analysis of Function Spaces
Much of my work contributes to the theory of a nonlocal model in continuum mechanics known as peridynamics. I have also conducted analysis of systems of hyperbolic conservation laws. My work has given me the chance to use variational methods and techniques from potential theory, harmonic analysis, and compensated compactness to analyze partial differential and integral equations.
For teaching information and a publication list, see my personal website (link on the right).