  This paper consists of two parts strictly related one to the other. The first
is a survey of important facts and leading problems concerning the applications
of differential geometry in studies on the functional architecture of the
visual system. The second part presents a model for the hypercolumns, which
originates from the symplectic model of the primary visual cortex by A. Sarti,
G. Citti and J. Petitot, the spherical model of hypercolumns by P. Bressloff
and J. Cowan and basic results of the conformal geometry of sphere. The first
part is designed for a mathematically oriented audience and provides
motivations for the model in the second part.
