Olivier Ramare: Emergence and relevance of bilinear decompositions for primes

This talk will retrace the main steps of the modern theory of prime
numbers and in particular how the combinatorial sieve combined with the
Dirichlet series theory to give birth to the modern representation of
the primes via a linear combination of terms, some of which being
"linear", while the other ones are "bilinear". This will lead us to the
recent developments of Green & Tao, Mauduit & Rivat, Tao, Helfgott,
and Bourgain, Sarnak & Ziegler.