Unprojection theory aims to analyze (and construct) complicated
commutative rings in terms of simpler ones. The talk will be
about joint work in progress with Christos Athanasiadis (Athens)
and Janko Boehm (Saarbruecken) that relates, on the algebraic
level of Stanley--Reisner rings, stellar subdivisions of
Gorenstein* simplicial complexes with the unprojection of
type Kustin--Miller.