  The mammalian hippocampus plays a principal role in producing a cognitive map
of space---an internalized representation of the animal's environment. The
neuronal mechanisms producing this map depend primarily on the temporal
structure of the hippocampal neurons' spiking activity, which is modulated by
the oscillatory extracellular electrical field potential. In this paper, we
discuss the integrative effect of the gamma rhythm, one of the principal
components of these oscillations, on the ability of the place cell ensembles to
encode a spatial map. Using methods of algebraic topology and statistical
physics, we demonstrate that gamma-modulation of neuronal activity generates a
synchronized spiking of dynamical cell assemblies, which enables learning a
spatial map at faster timescales.
