Connections between mathematics and neuroscience

International audienceI will discuss some of the relations between mathematics and neuroscience, in effect the neuroscience of visual perception of edges and textures. Starting from the question of knowing how the cortical representation of retinal images is organized, I will show that it leads in a very natural way to geometric concepts grounded in hyperbolic geometry, hence non-Euclidean, of the Poincaré disk et to ideas from the theory of the bifurcations of dynamic systems. These mathematical models predict specific types of neuronal activity that should become soon accessible to experimentation. Conversely the neurobiological phenomena that are represented by these models raise deep and difficult mathematical questions