The talk will take into account the space of curves as a Riemannian manifold with a metric, measuring the squared $L^2$ norm
of arc length derivatives of curve variations. Based on a suitable time discretization it will be described how to interpolate pairs of curves, smoothly extrapolate paths in this space, and how to approximate the associated covariant derivative as well as the curvature tensor. The convergence of the discrete calculus to the corresponding continuous calculus will be demonstrated.
