Mark Shusterman (Tel-Aviv University)
Intersection of finitely generated (Galois) groups (08/11/2017)

Howson's classical 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 (elementary) proof techniques. I will then report on an extension of the results to Demushkin groups (a class of groups that is of great importance in Galois theory). My proof has to do with another classical problem called Kaplansky's zero-divisor conjecture.

No preliminaries are assumed beyond basic familiarity with the free group.

The talk is based on joint works with Andrei Jaikin-Zapirain, and Pavel Zalesskii.