# Cocompact lattices on $$\tilde{A}_2$$ buildings.

Algebra/Geometry/Topology Seminar

#### by Anne Thomas

Institution: University of Sydney
Date: Fri 17th February 2012
Time: 11:15 AM
Location: Russell Love Theatre, Richard Berry

Abstract: Let K be the field of formal Laurent series over the finite field $$F_q$$, and let G be the group SL(3,K). We construct cocompact lattices of minimal covolume in G by extending work of Cartwright, Mantero, Steger and Zappa, which used cyclic algebras, and considering the action of finite groups of Lie type on the associated building. This is joint work with Inna (Korchagina) Capdeboscq and Dmitri Rumynin.