Mathematics of visual perception: a neurogeometrical approach

I will review the role of sub-Riemannian geometry in neurogeometry of the visual cortex (SE(2) group) and show how it is engendering visual perception. Particularly horizontal curves and geodesics will account for a number of geometric phenomena on the visual field. A mean field equation defined on the SE(2) geometry will model neural activity and its symmetry breaking will provide visual percepts. An open problem about heterogeneous neurogeometry will be preliminarily discussed. (Joint work with Giovanna Citti)