Seminar talk, 18 March 2015

The term "neurogeometry" had been proposed by J.Petitot in 1990 for the branch of neuroscience, which investigates different models of brain structures, mostly related with vision, in the language of differential geometry and differential equations. The structures are considered as continuum media with internal structure, described by properties of neurons. The approach is based on the principle of locality of visual neurons, whose excitation depends on energy density of light $\displaystyle{ I }$, coming to a small domain $\displaystyle{ D }$ of retina ("receptive field"). Many visual neurons work as linear filters (generalized functions with support $\displaystyle{ D }$) — their excitation is described by the integral of the intensity function $\displaystyle{ I }$ over $\displaystyle{ D }$ taking with some weight ("receptive profile").