Questions, Algorithms, and Computations
in Abstract Group Theory
May 21-24, 2013, TU Braunschweig
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.