| Tropical geometry is used to develop a new approach to the theory of discriminants and resultants in the sense of Gel'fand, Kapranov and Zelevinsky. The tropical A-discriminant, which is the tropicalization of the dual variety of a toric variety, coincides with the Minkowski sum of the row space of the given matrix A and of the tropicalization of the kernel of A. This leads to a positive formula for the extreme monomials of any A-discriminant. Joint work with Alicia Dickenstein and Eva Feichtner. |