seminar: Contact structures and coherent states in neurogeometry
speaker: Jean Petitot (CREA, Ecole Polytechnique)abstract: Many recent works have shown that visual primary cortical areas implement in their functional architecture sophisticated geometrical structures. In particular the pinwheel structure of V1 implements the contact structure of plane curves and even, if scale is taken into account, its symplectification. The sub-Riemannian geometry associated to this contact structure enables to explain well known Gestalt phenomena such as illusory contours. The functional architecture can also be modelled as a group structure G of Heisenberg type. As it operates upon neural receptive profiles performing a wavelet analysis of the signal, the theoretical frame for modelling naturally becomes that of coherent states on G in relation with sub-Riemannian geometry (geodesics, cut points, conjugate points, etc.). But one must be very cautious concerning the details of the neural implementation and look precisely at empirical data.
timetable:
Tue 5 Sep, 14:30 - 15:30, Aula Dini
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