One of the topological changes of state exhibited by some systems is called “monodromy”.  This can be found in quasi-linear molecules, atoms in a trap, a “swing-spring”, or a hydrogen atom in crossed fields.   A quantum manifestation of monodromy is a defect in the lattice of eigenvalues.  A dynamical manifestation of monodromy, which will be visible in both classical and quantum systems, will be described in this talk.  Especially we discuss how this phenomenon could be observed using a classical pendulum system or ultracold atoms.

(This lecture is rather more specialized, suitable for an audience of grad students and faculty.)