The term "Geometers" makes me think of Neal Stephenson's Anathem, which is just as will, since the article is about advanced orbits.
The picture at the start of the article looks like Lissajous patterns. And sure enough Lissajous orbits around lagrange points are a thing according to wikipedia.
This is really cool research, but to say "symplectic geometry, an abstract field of math that is generally far removed from messy real-world details" in the context of orbit planning is a gross mischaracterization. All serious solar system dynamics research happens in phase space not cartesian space, which means symplectic geometry - that is the orbital parameters are integrated instead of x,y,z. This amusingly named website has a fairly approachable description of what's happening : https://wiki.tfes.org/Symplectic_Integrators