Georgia Institute of Technology College of Sciences

There is a beautiful idea that one can study spaces by studying associated geometric objects. More specifically one can associate to a manifold (that is some space) a symplectic or contact manifold (that is the geometric object). The question is how useful is this idea. We will discuss this idea and related questions for subspaces (that is immersions and embeddings) with a focus on curves in the plane and knots in three space. If time permits we will discuss powerful new tools from contact geometry that allow one use this idea to construct invariants of knots and more generally embeddings and immersions in any space.