The Geometric Group Theory Unit explores the deep connections between algebraic and geometric structures in infinite groups. Our research focuses on the large-scale geometry of groups, emphasizing hyperbolicity, growth, and projection phenomena that arise naturally from spaces of negative or non-positive curvature. We integrate techniques from hyperbolic geometry, geometric topology, and combinatorial group theory to study families such as hyperbolic groups, mapping class groups, and fundamental groups of manifolds. Recent work has uncovered new phenomena in the growth rates of groups and introduced novel tools to analyze their algebraic and geometric behavior. We also employ computational methods to investigate group-theoretic and analytical structures of infinite groups.
