RTG workshop Information


Undergraduate workshop: June 4-15, 2012
Graduate workshop: June 18-22, 2012

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 every group this way, and then the challenge is to describe the corresponding geometric object.

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.