Caley graphs, Quasi-isometries, Fundamental Lemma of GGT, Bass-Serre theory, Free groups, amalgams, surface groups, Universal covers, Hyperbolic space, Nonpositive curvature and CAT(0) geometry, Hyperbolic groups, Simple complexes of groups, Coxeter groups, Artin groups, Graph products of groups, Actions on CAT(0) cube complexes. Examples of group actions on contractible polyhedra.
Prereq: Post-candidacy status in Mathematics Graduate Program, and permission of instructor. Not open to students with credit for 7821.01. This course is graded S/U.