Discriminants and root systems (A joint talk with the MPI-Oberseminar)

Gelfand, Kapranov and Zelevinskij have shown that the
Newton polytope of the classical discriminant of a polynomial
of degree $n$ is combinatorially equivalent to a $(n-1)$-dimensional
cube. Moreover they observed  that this cube  is  closely related to
the root system of type $A_{n-1}$. The purpose of my talk is to discuss
the this observation from the viewpoint of tropical geometry and
mirror symmetry. Our approach is motivated by some  applications to
other root systems.