Geometric group theory.  More specifically: coarsely non-positively curved spaces, broadly construed (hyperbolic spaces and their generalisations, CAT(0) cube complexes and median spaces and various generalisations and special cases, injective/hyperconvex spaces); classes of examples that interest me include mapping class groups of surfaces, Artin and Coxeter groups, cubical groups, free-by-cyclic groups, 3-manifold groups, etc.