Math 752 — Spring 2001 Seminar in Topology: Geometric Group Theory
Geometric Group Theory establishes links between geometrical notions (like space curvature, isoperimetric problems, growth of balls etc.) and algebraic properties of groups (like beeing abelian, free, nilpotent, amenable, etc.)
The aim of the course is to focus on few invariants (Dehn functions, growth, isoperimetric profils and heat decay) and to compute them for each of the eight 3-dimensional geometries of Thurston.
The course will include a classification of the eight 3-dimensional geometries (answering the question "Why only eight geometries?") and should give the students a geometric intuition of "what a nilpotent or solvable Lie group looks like."
IMPORTANT POINT: The course will be organized so that after a few presentation sessions, each student will choose a piece of the puzzle to study and present to the others.