  In this paper, we present a low overhead beam management approach for
near-field millimeter-wave multi-antenna communication systems enabled by
Reconfigurable Intelligent Surfaces (RISs). We devise a novel variable-width
hierarchical phaseshift codebook suitable for both the near- and far-field of
the RIS, and present a fast alignment algorithm for the RIS phase shifts and
the transceiver beamformers. Indicative performance evaluation results are
shown, verifying the effectiveness of the proposed approach in comparison with
various benchmark schemes.
