Some more geometry in the secondary fan

  A polyhedral subdivision of finitely many points A in R^d 
is a decomposition of its convex hull into non-overlapping 
polytopes with vertices in A.  It is regular if the polytopes 
are projections of facets of a polyhedron in R^{d+1}.  Gelfand,
Kapranov, and Zelevinsky introduced the secondary fan of A, 
which encodes all regular subdivisions of A. 

  I will talk on work with Postinghel and Villamizar that
explains another geometric interpretation of the secondary fan.
The points A give a curvilinear copy of the convex hull of
A in the probability simplex whose vertices correspond to A
which we call the real toric variety of A.  We consider 
possible Hausdorff limits of translations of this real toric
variety.  We show that the possible limits correspond to the 
cones of the secondary fan.  Our main tool is a study of 
sequences in the ambient space of the secondary fan.