RTG workshop Information
A few words about geometric group theory:
You have studied groups before, and you have probably learned that sometimes
you can view a group as the set of symmetries of a geometric object. In geometric group theory
we take this idea to its extreme: we think of
The groups we are talking about are typically infinite discrete groups, which can be described using generators and relations. (As a way to prepare for the workshop, try to recall whichever infinite groups you've encountered so far. How do you usually think about these groups?)
Lots of times, it is a geometric object that makes us start to think about a group in the first place, like in the case of knot groups, braid groups, or more generally any fundamental group. Other times groups arise as matrix groups, like SL_2(Z). Other times we try to come up with groups that have interesting geometries.
Check out this wikipedia page for more.