Mathematics & Statistics research seminar
Pizza and soft drinks will be served after the talk.
SPEAKER: Dr. Jeremy Macdonald
ABSTRACT: Group presentations give a way to define a group using some building blocks (generators) and rules according to which they interact (relations). Many important infinite groups can be described by finite presentations, which in principle provides a computer program all of the information it needs to perform computations in the group. However, even the most basic questions, such as "Is this group trivial?" can be undecidable. When such questions can be answered, we ask to determine the computational complexity of doing so.
We will provide an elementary introduction to algorithmic problems in groups and survey the current state of knowledge in the class of (infinite) nilpotent groups, including new results on low-complexity problems.