Appears in collection : Rational Points on Fano and Similar Varieties

Poonen and Voloch have conjectured that almost every degree d Fano hypersur- face in Pn defined over the field of rational numbers satisfies the Hasse principle. In joint work with T. Browning and P. Le Boudec, we establish this conjecture under the mild assumption that n d + 1. This talk is the first of two talks. Our goal in this first talk will be to introduce our main results and to present the strategy of the proof.