The Pukhlikov–Khovanskii theorem

Theorem of Kushnirenko and D.Bernstein on the number of solutions of a system of Laurent polynomial equations in terms of the volumes of their Newton polytopes can be interpreted as a formula for the intersection numbers of divisors in a projecive toric variety. In 1992 Pukhlikov and Khovanskii observed that the Kushnirenko theorem completely determines the cohomology ring of a smooth projective toric variety. I will speak about the Pukhlikov-Khovanskii theorem and, time permitting, will mention its further generalization to the case of spherical varieties, due to K.Kaveh.