Samuel Mellick: "Fixed price one for higher rank Lie groups and some products of groups"

mardi 10 oct. 2023, 10:30 → 11:30 Europe/Paris

In recent joint work with Mikolaj Fraczyk and Amanda Wilkens, it was shown that higher rank Lie groups and products of automorphism groups of regular trees have fixed price one. This immediately implies that all lattices in such groups have fixed price one (this was known for non-uniform lattices, due to Gaboriau). Additionally, by applying a theorem of Abert-M. or a theorem of Carderi (independently proved) we get uniform vanishing of rank gradient for any sequence of lattices in higher rank Lie groups, resolving a conjecture of Abert-Gelander-Nikolov.

 

In a follow up paper, I prove a generalisation of a criterion of Gaboriau for showing that a group has fixed price one. This gives an alternative proof for fixed price one for higher rank Lie groups (but not products of trees). It also applies to certain products of groups, which yields as a corollary fixed price one for SL(2,Q).

 

In this talk I will explain how the generalistaion of Gaboriau's criterion is proved. No prior knowledge of cost for topological groups will be assumed.