Partial Differential Equations and Spectral Theory

We investigate questions in partial differential equations (PDEs) and the spectral theory of differential operators, often in connection with geometric aspects. Our research spans topics such as:

• inverse problems,
• asymptotic distribution of eigenvalues,
• shape optimisation,
• functional calculus for non-self-adjoint operators,
• the Kato square root problem,
• problems with limited regularity.

Applications of these areas include quantum mechanics, string theory, and phenomena related to diffusion and absorption.