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# On a conjecture of Poonen and Voloch I: Probabilistic models for counting rational points on random Fano hypersurfaces

## Will Sawin

Poonen and Voloch have conjectured that almost every degree $$d$$ Fano hypersurface in $$\mathbf P^n$$ 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.