16:00-17:30 on Monday (8th, 15th, 22th April)

VooV Meeting ID: 785-1518-0192

PW: 578337

16:00-17:30 on Wednesday (10th, 17th, 24th April)

VooV Meeting ID: 414-4918-3909

PW: 578337

Abstract: Automorphism groups of finitely generated free groups have been studied since the work of Nielsen in the 1920s, who first proved that these groups are finitely generated, and even finitely presented. Over the twentieth century, the viewpoint has progressively switched from combinatorial group theory to geometric group theory. A cornerstone in this study was the construction by Culler and Vogtmann, in the 80s, of Outer space, a contractible space equipped with an action of Out(Fn) (the outer automorphism group of a free group of rank n), analogous to the action of a surface mapping class group on its Teichmüller space. In this mini-course, I will introduce Outer space, describe its topology and its geometry, and explain how it can be used to prove structural theorems about the group Out(Fn), keeping in mind the analogy with Teichmüller spaces. I will also present several developments that took place in the past three decades, in particular the quest for negative curvature features in Out(Fn), Outer space, and related spaces.