CAT(0) cube complexes in geometric group theory

Daniel Wise, McGill University
Fine Hall 314

CAT(0) cube complexes are high-dimensional generalizations of trees that have emerged as increasingly central objects in combinatorial and geometric group theory. I will describe their prominent geometric properties and explain how cube complexes often arise from infinite groups - the latest examples being the fundamental groups of hyperbolic 3-manifolds. I'll then indicate a "grand plan'' for understanding many groups from this viewpoint.