Foundations of Algorithmic Verification and
Theoretical Computer Science; in particular:

Decision, control, and synthesis problems for discrete and continuous
linear dynamical systems (using tools from number theory,
Diophantine geometry, algebraic geometry)

Automated verification of real-time, probabilistic, and infinite-state systems
(e.g. model-checking algorithms, synthesis problems, complexity)

Logic and applications to verification

Automated software analysis

Concurrency