Algebraic knot theory

A topological knot is given by an embedding of the circle in the Euclidean three-space and two knots are equivalent if the embeddings are isotopic, meaning that they can be interpolated by a continuous family of embeddings. The algebraic equivalent of a knot, is the embedding of a (rational) curve into a projective three-space and there is also a natural notion of algebraic isotopy. In this talk I will explain how to study these objects via classical secant varieties of curves. This is joint work with Mario Kummer.