  Much has been learned about string theory over the last few years by studying
properties of cycles and branes in a given background geometry. Here we discuss
three situations (quantum volume, attractor flows/D-brane stability, and
dynamical topology change) in which cycles in a Calabi-Yau background evolve
and/or degenerate in some manner, yielding various insights into aspects of
quantum geometry. Based in part on talk given at Strings 2000.
