  In this lecture I review how a matrix/Azumaya-type noncommutative geometry
arises for D-branes in string theory and how such a geometry serves as an
origin of the master nature of D-branes; and then highlight an abundance
conjecture on D0-brane resolutions of singularities that is extracted and
purified from a work of Douglas and Moore in 1996. A conjectural relation of
our setting with `D-geometry' in the sense of Douglas is also given. The
lecture is based on a series of works on D-branes with Shing-Tung Yau, and in
part with Si Li and Ruifang Song.
