  Recently, it has become clear that neighboring multiple vacua might have
interesting consequences for the physics of the early universe. In this paper
we investigate the topography of the string landscape corresponding to complex
structure moduli of flux compactified type IIB string theory. We find that
series of continuously connected vacua are common. The properties of these
series are described, and we relate the existence of infinite series of minima
to certain unresolved mathematical problems in group theory. Numerical studies
of the mirror quintic serve as illustrating examples.
