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Arithmetic, Dynamical systems (Ergodic Theory, Small denominator problems), Number Theory (Diophantine approximation, Metric number theory)
Arithmetic, Algebra, Algebraic geometry, Coding theory, Commutative algebra, Computational number theory, Cryptology (Elliptic- and hyperelliptic curves), Data security, Group theory, Number Theory, Public-key encryption (Elliptic and hyperelliptic curves)