Research

My main research directions are on the intersection of pure analysis, mathematical physics, applied mathematics, and numerical analysis.

My current interests are mainly in foundations, applications and numerical methods of spectral theory and spectral geometry, and include the following ongoing projects.

Spectral geometry of Dirichlet-to-Neumann maps

Spectral geometry of Laplace, Dirac, Maxwell and Lamé operators

Universal and isoperimetric estimates, and null varieties

Non-self-adjoint operators and operator pencils

Exterior problems, eigenvalues, and resonances on manifolds with regular ends and unbounded domains