Geometric group theory is an area of math that closely interacts with low-dimensional topology and hyperbolic geometry. The central idea of geometric group theory is the study of finitely generated groups as geometric objects. In the talk, I plan to introduce the graph of a group; the notions of quasi-isometry, delta-hyperbolicity, and n-thickness; and to discuss the Milnor-Svarc Theorem. The talk will contain illustrative examples as well as open questions in the area.
This talk should be accessible to everyone -- elementary algebra and topology recommended.