Mathematics Colloquium

In favorable circumstances, topological 4-manifolds can be classified. In contrast, smooth 4-manifolds remain poorly understood. Several hard questions (eg the Poincare conjecture) in 4-manifold topology boil down to asking whether there can be distinct smooth (sub)manifolds with the same topological type; such manifolds are called exotic. In this talk I will discuss a few methods to demonstrate exotic phenomena, and comment on how these methods might be adapted towards addressing some of these questions.