Thor Wittich

Results of Shastri allow us to study knots, i.e. embeddings S^1 -> S^3, within the world of algebraic geometry. This has already been used successfully, as it lead to Gupta's counterexamples for Zariski cancellation in positive characteristic. Explaining this will be the first part of the talk. Afterwards, we consider algebraic knots through the lense of motivic homotopy theory, which is based on ongoing joint work with Matthias Wendt. Here I will mainly try to indicate how certain motivic invariants of algebraic knots relate to the study of the original topological knot, but also to questions surrounding Zariski cancellation. We will not assume familiarity with motivic homotopy theory.