Singularities arise naturally in algebraic geometry when trying to classify algebraic varieties. However, they are also a rich source of examples in other fields, particularly in topology. We will explain how complex hypersurface singularities give rise to knots and links, some of which are manifolds that are homologically spheres but not topologically (Poincare homology spheres), or manifolds that are homeomorphic to spheres but not diffeomorphic to them (exotic spheres). The talk should be accessible to anyone with some basic knowledge of differential and algebraic topology, although even that is not strictly necessary. Speaker(s): Takumi Murayama (UM)