[Travail en commun avec Sarnak]
Firstly, I will introduce a recent conjecture of Peter Sarnak
on the distribution of primes on orbits,
which may be viewed as a non-abelian extension of Dirichlet's theorem,
the Hardy-Littlewood
prime k-tuple conjecture, Schinzel's hypothesis, etc.
After that, I will report a joint result with
Sarnak concerning almost prime solutions to ternary quadratic equations.