Flatness 

-> Discussion of a good notion of family of algebraic varieties
   * Definition of flat family of projective varieties via Hhilbert polynomials
   * Flat module, general flat family 
   * Outline of relation
  
-> Flat families parametrized by smooth curves

-> Flat families given by toric deformations

-> Connection to Groebner bases

-> Regular triangulations and initial ideals
   * Unimodular triangulations and square-free initial ideals

-> Review the BGT Theorem, and some open questions.