On the linearity of lattices in affine buildings
Groups acting on CAT(0) spaces September 27, 2016 - September 30, 2016
Location: MSRI: Simons Auditorium
CAT(0) space
negative curvature manifolds
Riemannian geometry
buildings and complexes
affine buildings and cells
algebraic combinatorics
Bruhat-Tits construction
automorphism groups
Margulis superrigidity
discrete group actions
57-XX - Manifolds and cell complexes {For complex manifolds, see 32Qxx}
58D05 - Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]
20E36 - Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45]
20Exx - Structure and classification of infinite or finite groups
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 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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14619
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