More than 100 years ago, Dehn proposed his famous problems on abstract groups: the word problem, the conjugacy problem and the isomorphism problem. It is long known that all three problems are undecidable in general. Nonetheless, they have inspired a rich theory of computations in abstract group theory.

There are various classes of groups, such as word hyperbolic, automatic and polycyclic groups, for which many natural decision problems are solvable. On the other hand, there are constructions of groups with unexpected properties such as the Tarski or Dehn monsters. Most problems are undecidable in these monsters. It remains open to understand both of these opposite ends and where the boundary between them lies.

Recently, the new research topic of cryptography based on abstract groups has been invented. This topic requires fundamental knowledge about the complexity and the efficiency of various algorithms on abstract groups. This has produced a new interest in computations with abstract groups.

Our aim is to combine researchers form the areas of abstract group theory, computer science and algebraic geometry to obtain new advances in algorithmic group theory.