Modular and automorphic forms of various types, including: Maass forms, Jacobi forms, vector-valued modular forms, Hilbert modular forms (and combinations of the above)
Computational number theory
Analytic Number Theory
Computational spectral theory (for hyperbolic surfaces)
Dynamical systems, transfer operators and the thermodynamical formalism
Mathematical aspects of (arithmetic) Quantum Chaos
Hilbert - Maass forms