Department of Ergodic Theory and Dynamical Systems
Research Topics:
Locally Hamiltonian systems, interval exchange transformations, and dynamics on surfaces:
- Locally Hamiltonian systems and their perturbations, generalized interval exchange transformations
- Locally Hamiltonian systems and translation flows
- Interval exchange transformations and their generalizations, and flows on surfaces
Dynamics and ergodic theory in number theory:
- Dynamical properties of Furstenberg systems of arithmetic multiplicative functions
- Applications of ergodic theory in number theory
- Sarnak’s conjecture
- Prime Number Theorem in dynamical systems
- Boshernitzan’s orthogonality problem
- Furstenberg systems of aperiodic multiplicative functions
General ergodic theory and spectral properties:
- Unitary and Koopman representations
- Relative ergodic theory
- Ergodic and spectral properties
Hyperbolic and chaotic dynamics, smooth systems:
- Hyperbolic dynamics
- Nilmanifolds
- Circle diffeomorphisms
- Chaotic dynamics
Symbolic systems:
- B-free systems
- Toeplitz systems
- Hereditary and sandwich systems
Applications of dynamical systems in other areas of mathematics:
- Functional equations and their applications
- Prime number theorems
- Applications of dynamical systems in combinatorial problems