Introduction to Combinatorial and Geometric Group Theory

Combinatorial and geometric group theory aim to relate algebraic properties of groups with combinatorial, geometrical and topological properties of spaces on which such groups act. In this project we studied fundamental topics of these theories such as the Bass-Serre theory of groups acting on trees, the Guba-Sapir diagram groups, the Banach-Tarski paradox and amenable groups, Gromov hyperbolic groups and automata groups. We studied tools such as the Cayley graph, 2-complexes and their fundamental group, Van Kampen diagrams for words, Gromov’s word growth, Dehn’s decision problems, regular languages and finite state automata.