Describing Amoebas

  Amoebas and coamoebas are curvilinear cousins of tropical varieties,
which consist of the lengths and the arguments, respectively, of an 
algebraic subvariety of the torus.  Purbhoo's Nullstellensatz shows
that the amoeba of a variety is the intersection of amoebas of 
hypersurfaces coming from its ideal.  Subsequent work has involved
approximating amoebas and showing that zero-dimensional amoebas are
the finite intersection of hypersurface amoebae.  

  Starting from the observation that amoebas and coamoebas are 
semi-algebraic sets, I propose the problem of finding a description
of these tropical cousins as semi-algebraic sets.  This appears hard, 
even for curves in low-dimensional tori.  I will also discuss progress 
with Nisse towards classifying those amoebas that are the finite 
intersection of hypersurface amoebas.