The notion of a (uni) versal building associated with a point in the Hitchin base is introduced.
The universal building is a building equipped with a harmonic map from the universal cover …

For all algebraic groups over non-Archimedean local fields, the bounded cohomology
vanishes. This follows from the corresponding statement for automorphism groups of Bruhat …

In the Labourie-Loftin parametrization of the Hitchin component of surface group
representations into SL (3, R), we prove an asymptotic formula for holonomy along rays in …

Abstract Affine Bruhat–Tits buildings are geometric spaces extracting the combinatorics of
algebraic groups. The building of PGL PGL parameterizes flags of subspaces/lattices in or …

A masure (aka affine ordered hovel) I is a generalization of the Bruhat-Tits building that is
associated to a split Kac-Moody group G over a non-archimedean local field. This is a union …

In this work we describe horofunction compactifications of metric spaces and finite-
dimensional real vector spaces through asymmetric metrics and asymmetric polyhedral …

We study eigenfunctions of the spherical Hecke algebra acting on L^ 2 (Gamma_n
backslash G/K) where G= PGL (3, F) with F a non-archimedean local field of characteristic …

We develop the theory of algebraic groups over real closed fields and apply the results to
construct a geometric object $\mathcal {B} $ and to prove that $\mathcal {B} $ is an affine …

Masures were introduced in 2008 by Gaussent and Rousseau in order to study Kac-Moody
groups over local fields. They generalize Bruhat-Tits buildings. In this thesis, we study the …

We study joint eigenfunctions of the spherical Hecke algebra acting on $ L^ 2
(\Gamma_n\backslash G/K) $ where $ G=\text {PGL}(3, F) $ with $ F $ a non-archimedean …