Intersection of finitely generated (Galois) groups
Howson's theorem says that the intersection of two finitely generated subgroups of a free group is finitely generated.
Hanna Neumann conjectured a bound on the number of generators of the intersection, that after many years of works, has been established independently by Friedman and Mineyev.
I will discuss the history of this problem, surveying the proof techniques. I will then report on a new proof of the stengthened Hanna Neumann conjecture by Jaikin-Zapirain, and show that it generalizes to Demushkin groups (a class of pro-p groups that is of great importance in Galois theory).
No preliminaries are assumed beyond basic familiarity with the free group.
This is a joint work with Andrei Jaikin-Zapirain.