On the linearity of lattices in affine buildings
Location: MSRI: Simons Auditorium
negative curvature manifolds
buildings and complexes
affine buildings and cells
discrete group actions
One of the most prominent class of CAT(0) spaces is the class of Affine Buildings.
In dimension 1, an affine building is nothing but a tree. In dimension 3 and higher (irreducible) affine buildings are always classical, that is they are the Bruhat-Tits buildings of algebraic groups over valued fields. In dimension 2 there are loads of exotic (ie, non-classical) buildings. Some are intimately related with some sporadic finite simple groups. Many have a cocompact group of isometries.
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