Speaker
Naomi Andrew
(Laboratoire de Mathématiques d’Orsay)
Description
Groups encode symmetries, and their automorphism groups encode the symmetries of the group themselves. So we can ask when "nice" properties of a group imply "nice" properties of its automorphisms. On the positive side, mapping class groups, GL(n,Z) and Out(F_n) are all finitely presented (in fact a stronger property: Type VF), and this can be analysed geometrically, using spaces built from actions of the original group. On the other hand, the Baumslag–Solitar group BS(2,4) is finitely presented, yet its outer automorphism group is not even finitely generated (and there is also a geometric explanation for this). I will discuss some new results in this area.
Author
Naomi Andrew
(Laboratoire de Mathématiques d’Orsay)