Legendrian Knots and Their Fillings -
To a topologist, knots are embeddings of a circle into 3-dimensional space, and we can learn a lot about a knot from studying the surfaces that it bounds. If we endow 3-space with a contact structure, i.e. a plane field satisfying certain technical conditions, then we can ask that our knots and surfaces respect this structure. In this talk, I will describe the kinds of knots that appear in contact topology and discuss techniques for constructing and visualizing the surfaces that they bound.