# Olivier Ramare: Emergence and relevance of bilinear decompositions for primes

**Time: **
Wed 2019-03-13 11.00

**Location: **
F11

**Lecturer: **
Olivier Ramare

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.