Complex Analysis

• Interpolation, sampling, and uniqueness problems in spaces of holomorphic functions (Hardy, model spaces, Bergman, Dirichlet, Fock, Korenblum, de Branges(-Rovnyak))
• Random aspects
• Model spaces
• Holomorphic dynamics in several variables

Functional and Harmonic Analysis

• Toeplitz operators
• Hardy-type uncertainty principles
• Non-harmonic Fourier series
• Applications to PDEs and signal theory

Control and Observation of Systems Described by PDEs

• Observability inequalities via Carleman inequalities or harmonic analysis techniques
• Reachable spaces for parabolic systems
• Time-optimal control