In 2021, Burger, Iozzi, Parreau, and Pozzetti defined a compactification of higher Teichmüller spaces using the real spectrum compactification. Their work is inspired by Brumfiel's compactification of classical Teichmüller space, where trees of non-Archimidean hyperbolic planes arise. For higher rank Lie groups, anologues objects show up, namely affine buildings over non-Archimidean fields. The end goal of this reading group is to understand the affine buildings from the [BIPP] compactification. We will learn about different types of affine buildings, and close with the ones arising in [BIPP], i.e. Lambda-buildings.

We will begin with Brumfiel's article about trees of non-Archimidean hyperbolic planes. We will then move on to the work of Kleiner and Leeb, where explicit constructions of R-buildings are given. Next is Parreau's work, where she gives an explicit model of affine buildings over GL(n,F), where F is allowed to be non-Archimidean. We close with Kramer and Tent's article, where a construction of Lambda-buildings is given.