RESEARCH GROUP

GEOMETRY

We are excited to welcome Isobel Davies to our team, who joined us in January 2021.
She will be working on her PhD under joint supervision of Petra Schwer and Linus Kramer (at WWU Münster).
Isobel, a warm welcome to you and we wish you a great start in your new phase!

Bram Bekker is developing an interactive website that helps visualizing spherical and affine buidlings. 
This is really cool!

Go play with the impressive pictures on The Buildings gallery!

The preprint "Twisted conjugacy in soluble arithmetic groups" by Paula Macedo Lins de Araujo and Yuri Santos Rego has been recently uploaded to the arXiv!

Link to the paper: arXiv:2007.02988.

Abstract:
We investigate the ongoing problem of classifying which S-arithmetic groups have the so-called property R∞. While non-amenable S-arithmetic groups tend to have R_∞, the soluble case seems more delicate. Here we address Borel subgroups in type A and show how the problem reduces to determining whether a metabelian subgroup of GL₂ has R_∞. For higher solubility class we show how automorphisms of the base ring give R_∞. Our results yield many families of soluble S-arithmetic groups with R_∞ but we also exhibit metabelian families not manifesting it. We formulate a conjecture concerning R_∞ for the groups in question, addressing their geometric properties and algebraic structure.