Lecture 4.  Reality and the Viro Construction

-> Solving equations again
   * Restrict to the case of a polytope, and show that the 
      Hilbert polynomial is the Erhart (spelling) polynomial.
      Conclude that the projective degree is n! volume of polytope
   * Kouchnirenko's Theorem
   * Sturmfels Reality Theorem
   * Viro's construction

Lecture 4 Grassmann Varieties

-> The problem of four lines

-> Ramification of linear series and the Wronski map

-> The Grassmann variety
   * Manifold via local coodinates
   * Manifold via Homogenous space
   * The Pluecker embedding