Research summary
Low-dimensional topology is the branch of pure mathematics that is concerned with understanding 3D and 4D geometric and topological objects and the connections between them. As Canada Research Chair in Low-Dimensional Topology, Dr. Duncan McCoy is studying this area of math.
He and his research team are organizing their work around two main themes. The first will explore Dehn surgery, an operation for modifying 3D manifolds that has been the source of major questions and advances in low-dimensional topology. (In simple terms, a manifold is a space that looks flat and smooth when you zoom in on it, even if it might have a more complex global shape.) The second theme involves understanding the properties of smooth 4-manifolds that bound a specific 3-manifold. This second focus is motivated by questions from the theory of analytic singularities, which deals with the study of singular points in complex analytic functions and their properties.