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Abstract

Joint work with Pierre-Emmanuel Caprace
Kac-Moody groups over finite fields are finitely generated groups.  
Most of them can naturally be viewed as irreducible lattices in  
products of two closed automorphism groups of non-positively curved  
twinned building. Using some weak hyperbolic properties of non  
virtually abelian Coxeter groups, we prove that these lattices are  
simple if the corresponding buildings are (irreducible and) not of  
affine type (i.e. they are not Bruhat-Tits buildings). In fact, many  
of them are finitely presented and enjoy property (T). Our arguments  
explain geometrically why simplicity fails to hold only for affine  
Kac-Moody groups (i.e. arithmetic groups). If time permits, we will  
also explain how we prove that a nontrivial continuous homomorphism  
from a completed Kac-Moody group is always proper, and that Kac-Moody  
lattices fulfill conditions implying strong superrigidity properties  
for isometric actions on non-positively curved metric spaces.