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 Laplace, Dirac, Maxwell and Lame operators, and of Dirichlet-to-Neumann maps

Universal and isopermetric estimates, and null varieties

Non-self-adjoint operators and operator pencils

Theory and numerics for eigenvalues and resonances on manifolds with regular ends

Foundations of numerical analysis

In recent years, I participated in organising the following events: