# Intersection of finitely generated (Galois) groups

Seminar

Speaker

Mark Shusterman (Tel Aviv University)

Date

08/11/2017 - 11:30 - 10:30Add to Calendar

`2017-11-08 10:30:00``2017-11-08 11:30:00``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.``Third floor seminar room``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Place

Third floor seminar room

Abstract

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.

Last Updated Date : 30/10/2017