Geometrical aspects of infinite dimensional and discrete Integrable systems; ; Pentagram and associated maps; Discrete moving frames and invariants; Poisson geometry; Adler-Gel'fand-Dikii brackets; Differential Invariants and Invariant Differential and difference evolutions, specially their relationship with infinite and discrete Hamiltonians; Moving frames and discrete moving frames, and applications; Projective and parabolic Geometry; Applications to image processing; Mathematics and applications in general.