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The only prerequisite knowledge will be a passing familiarity with simplicial complexes, but knowledge of Coxeter groups and Lie groups will help with motivation.

Buildings are particular simplicial complexes usually related to (simple) Lie groups. Geometrically, buildings are to n-dimensional manifolds as infinite graphs are to the real line, where buildings and graphs have branch points. In the two special classes I will talk about, spherical buildings are buildings made by gluing together spheres, while Euclidean buildings are made by gluing Euclidean spaces.

From a Lie group perspective, the simplices of the spherical buildings are parabolic subgroups of a Lie group (ie subgroups containing a Borel subgroup). A parabolic subgroup P is a face of P' if P contains P' (notice the reversal in ordering). For Euclidean buildings, the simplicies can be represented as special subgroups of a Lie group over a field with a valuation, but this takes more work to define.

Since the pure axiomatic approach can be dry, I will focus on the examples related to the simplest case of the general linear group GL(n), and try to relate the geometry to the Lie theory whenever possible. If time allows, I will mention some applications to representation theory.