Corina Ciobotaru

The first part of my talk gives a brief introduction to Euclidean buildings. In the second part, I introduce the new notion of a strongly regular hyperbolic automorphism of a locally finite Euclidean building X and I prove two main properties of such an element: the existence and the peculiar dynamics on the spherical building at infinity of X. Those properties are used in the third part where some applications are presented:  the characterization of Gelfand pairs in the setting of Euclidean buildings, Gromov's flat closing problem and the construction of non-abelian free automorphisms subgroups for general buildings. Some of these results are joint work with Pierre-Emmanuel Caprace.