Affine buildings for algebraic groups over real closed fields

We start by giving a bird's eye view of the theory of symmetric spaces, the theory of buildings and their connections. We will then sketch a construction of non-discrete affine buildings associated to semisimple algebraic groups over real closed fields. The construction relies on a semi-algebraic description of symmetric spaces and a transfer principle for real closed fields from model theory. Actions on these buildings naturally show up up in the boundary of real spectrum compactifications of character varieties.