Low-dimensional topology with a view towards embedding problems in affine algebraic geometry

In this talk, I present classical questions about polynomial maps from the complex line C into complex
spaces such as C^m and affine algebraic groups from the perspective of low-dimensional topology.
On one hand, we study singularities of such maps and their deformations. On the other hand, we consider
embeddings of the complex line C into complex spaces.
Throughout the talk, I will focus on how ideas from knot theory enter the proofs in algebraic geometry.