In the early 1960's the meteorologist E.N. Lorenz set out to
search, systematically, for a simple example of a system of ODE's which
exhibited the kind of unpredictable behavior which had long plagued
weather forcasters. The system of 3 ODE's that he found was “almost”
linear, and soon became famous in studies of chaos. Lorenz knots and links
are the periodic orbits in the flow associated to his equations. Recently,
they reappeared (totally unexpectedly) in the work of Etienne Ghys as the
closed orbits in the so-called modular flow on the manifold PSL(2,R)/PSL(2,Z).
We will discuss some of their very interesting properties, and the new
questions that occur to a knot theorist as a result of Ghys’ discoveries.