Dynamical systems, which have been studied in their own right, have also
been developed into a powerful tool to answer number theoretic and
(especially infinite) combinatorial questions. On the other hand many
questions concerning (discrete) dynamical systems are of a number theoretic or
combinatorial nature. Prominent examples are Margulis' proof of the
Oppenheim conjecture, or Furstenberg's proof of Szemerédi's
theorem. Other examples are given by Bourgain's ergodic theorems on
subsets of the integers, where methods from classical analytic number theory
play an important rôle. The results of Green and Tao on the existence of
arbitrarily long arithmetic progressions of prime numbers show the
strength of the interplay between combinatorial, number theoretic, and
dynamical methods and ideas. A further recent result in that context was the
solution of the classical Gel'fond conjectures on the sum-of-digits of
primes and squares by Mauduit and Rivat. The results of Adamczewski and
Bugeaud, which give a lower bound for the complexity function of the digital
expansion of algebraic irrationals, give a further prominent example for the
combination of combinatorial and Diophantine techniques.

From this short description, it is clear that the three areas have a strong and
fruitful interaction. The main aim of the proposed programme is to bring
together researchers from these areas, in order to intensify this interaction.
Send any questions to
e-mail: Restore Frames