Geometric/Global/Applied Analysis, Analysis on Non-compact and Singular Manifolds, Partial Differential Equations, Pseudo-Differential Operators, Mathematical Physics, and Scientific Computing.
These include: General Elliptic Boundary Value Problems, Asymptotic Theory, Spectral Theory (for selfadjoint and non-selfadjoint operators), Theory of Analytic and Singular Perturbations, Scattering Theory, Spectral Determinants (zeta-regularized determinants of Laplacians on non-compact/singular manifolds), related Numerical Methods and mathematical analysis of their stability and convergence.