On the linearity of lattices in affine buildings
Groups acting on CAT(0) spaces September 27, 2016  September 30, 2016
Location: SLMath: Eisenbud Auditorium
CAT(0) space
negative curvature manifolds
Riemannian geometry
buildings and complexes
affine buildings and cells
algebraic combinatorics
BruhatTits construction
automorphism groups
Margulis superrigidity
discrete group actions
54C40  Algebraic properties of function spaces in general topology [See also 46Exx]
0111  Research data for problems pertaining to history and biography
55R35  Classifying spaces of groups and $H$Hspaces in algebraic topology
20Exx  Structure and classification of infinite or finite groups
00A35  Methodology of mathematics {For mathematics education, see 97XX}
14619
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 BruhatTits buildings of algebraic groups over valued fields. In dimension 2 there are loads of exotic (ie, nonclassical) buildings. Some are intimately related with some sporadic finite simple groups. Many have a cocompact group of isometries.
Bader. Notes

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