**Monday 24 June 2024**

**15:00–16:30***

**Erik Lindell (Institut de Mathématiques de Jussieu – Paris Rive Gauche)** — *Stable cohomology of the IA-automorphism group*

The group Aut(F_{n}), where F_{n} is the free group on n generators, is an object of fundamental interest in low dimensional topology, where it appears as a kind of mapping class group of a wedge of circles. The IA-automorphism group, denoted IA_{n}, is the subgroup of Aut(F_{n}) consisting of those automorphisms which act as the identity on the abelianization of F_{n}. From the perspective of low dimensional topology, it is thus an analogue of the Torelli group of a surface. In comparison to Aut(F_{n}), our understanding of IA_{n} is still very limited. For example, we do not know whether it is finitely presented in general. More generally, we know very little about the (co)homology of IA_{n}, in degrees above one. In this talk I will review recent results concerning the "stable" part of the (co)homology, i.e. the cohomology in degrees small enough compared to the number of generators n.

* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.