Polytopes and Polynomial Systems
Frank Sottile
13 February 2006

   The exponent of a monomial involving n variables is an integer
vector in Z^n.   The set of exponents in a polynomial in n variables
is its support, and their convex hull is its Newton polytope.
Many questions and answers concerning zeroes of multivariate 
polynomials are best expressed in terms of the discrete structures
of support and Newton polytope.  The same is true for algorithms
and constructions involving multivariate polynomials.

  In this talk for a general audience from discrete mathematics,
I will explain some of this relation between polynomials
and polytopes, and give examples of how these structures are 
used to answer questions involving zeroes of multivariate polynomials.