Combinatorial and Geometric Group Theory

Groups are the mathematical objects that capture the structure of symmetry.  One modern approach to the study of infinite groups is to apply combinatorial and geometric tools.  For a flavour of these techniques, you can scan the book “Office Hours with a Geometric Group Theorist”, edited by Matt Clay and Dan Margalit, 2017 (ISBN 9780691158662).  Projects may be expository or include original research.  Specific topics may include: groups and their graphs; the geometry of automorphism groups of groups; groups, algorithms and machines.