Knots and spinors in 3-manifolds

We will introduce some techniques to address the following question: what type of topological structures emerge in the nodal sets of eigenfunctions of Dirac operators on compact manifolds? To illustrate these ideas, we will show that, for the Dirac operator on the round 3-sphere and the flat 3-torus, any given knot and link type arises as nodal set of the spinor components of an infinite number of eigenfunctions. These structures appear at small scales and sufficiently high energies.