Marco Linton (Oxford) : The coherence of one-relator groups

(Joint work with Andrei Jaikin-Zapirain.) A group is said to be coherent if all of its finitely generated subgroups are finitely presented. In this talk I will sketch a proof of Baumslag’s conjecture that all one-relator groups are coherent, discussing connections with the non-positive immersions property and the vanishing of the second L^2 Betti number.