Koiran + Geometric Topology implies "Knottedness is in NP"

In this seminar I will discuss the details of the result that knottedness is in NP assuming the generalized Riemann hypothesis. The main part of the work is to properly understand Koiran's construction that solvability of a system of algebraic equations is in AM. It is also uses one major result in geometric topology due to Kronheimer and Mrowka which can be accepted without serious study, although it is worth appreciating where it came from.