Lilian Matthiesen, Université de Bristol (Royaume Uni)

Pseudorandomness of the divisor function and an introduction
to Green and Tao's "nilpotent Hardy-Littlewood method"

In this talk we will survey the methods Green and Tao developed to study
linear equations in primes, and show how these methods may be employed
to deduce asymptotics for a class of divisor problems. This class includes,
for instance, correlations Σ_{n,r ≤ N} d(n) d(n+r) d(n+2r)... d(n+kr) of the divisor
function along arithmetic progressions of fixed length.