Counting roots of polynomial systems

Given n generically chosen polynomials of n variables, one expects that there are only finitely many common roots. Then a natural question is to count the exact number of these common roots without having to solve the system of equations. It turns out that this number is given by first taking the Newton polytopes of the polynomials, then computing their mixed volume, which is a quantity in convex geometry introduced by Minkowski. This result is now known as the Bernstein-Khovanskii-Kushnirenko Theorem. In the talk I will present an elementary proof of this theorem as well as some interesting related facts.