I am interested in nonlocal differential and difference equations.  I have studied such problems both in the context of nonlocal boundary value problems but also in the context of fractional calculus (both discrete and continuous), which involves inherently nonlocal operators.  I also have an interest in regularity theory for elliptic PDEs and minimizers of variational problems, and I am particularly interested in problems that involve rough or discontinuous coefficients and how such coefficients affect the regularity of any solution or minimizer.