With T. Nevins.  W-Symmetry of the Adelic Grassmannian.
We give a geometric construction of the W1+∞-vertex algebra as the infinitesimal form of a factorization structure on an adelic Grassmannian. This gives a concise interpretation of the higher symmetries and Backlund-Darboux transformations of the KP hierarchy and its multicomponent extensions in terms of a version of "W1+∞-geometry": the geometry of D-bundles on smooth curves, or equivalently torsion-free sheaves on cuspidal curves.