The Shards of $\omega$ Centauri
  We use the SDSS-Gaia catalogue to search for substructure in the stellar
halo. The sample comprises 62\,133 halo stars with full phase space coordinates
and extends out to heliocentric distances of $\sim 10$ kpc. As actions are
conserved under slow changes of the potential, they permit identification of
groups of stars with a common accretion history. We devise a method to identify
halo substructures based on their clustering in action space, using metallicity
as a secondary check. This is validated against smooth models and numerical
constructed stellar halos from the Aquarius simulations. We identify 21
substructures in the SDSS-Gaia catalogue, including 7 high significance, high
energy and retrograde ones.
  We investigate whether the retrograde substructures may be material stripped
off the atypical globular cluster $\omega$~Centauri. Using a simple model of
the accretion of the progenitor of the $\omega$~Centauri, we tentatively argue
for the possible association of up to 5 of our new substructures (labelled Rg1,
Rg3, Rg4, Rg6 and Rg7) with this event. This sets a minimum mass of $5 \times
10^8 M_\odot$ for the progenitor, so as to bring $\omega$~Centauri to its
current location in action -- energy space. Our proposal can be tested by high
resolution spectroscopy of the candidates to look for the unusual abundance
patterns possessed by $\omega$~Centauri stars.
