PUBLIC TALK: Maths & Stats Colloquium

Groups are mathematical objects that abstractly capture the concept of symmetry. Two groups are isomorphic if they essentially describe the same data, but they might be given with respect to different frames of reference. More specifically, two groups are isomorphic if there is a 1-to-1 correspondence between their elements that preserves the group operations. The group isomorphism problem is a decision problem that asks whether two given groups are isomorphic. This problem is of interest in theoretical computer science (with focus on the complexity of the problem) and in computational group theory (with focus on practical algorithms). My talk will survey some known results and comment on some recent new results, covering both complexity theory and practical applications to computer algebra systems.