Buildings Workshop 2026

Abstracts

Sira Busch

Title: Local-to-Global Rigidity of Bruhat-Tits Buildings

Abstract:A vertex-transitive graph X is called local-to-global rigid if there exists a natural number R such that every other graph, whose balls of radius R are isometric to the balls of radius R in X, is covered by X. In 2016 it was shown by De La Salle and Tessera that the 1-skeleton of an affine Bruhat-Tits building of type Ã_n, for n at least 3, is local-to-global rigid if and only if the underlying field has characteristic 0. In this talk I will describe how Amandine Escalier, Hendrik Van Maldeghem and me showed that this also holds for affine Bruhat-Tits buildings of other types.


Corina Ciobutaro

Title: Generic Chambers, Barycenters, and Boundaries of Affine Buildings

Abstract: Based on two joint papers with Corentin Le Bars, this talk explores the interplay between the geometry of affine buildings and the dynamics of groups acting on their boundaries. We discuss generic triples of antipodal chambers, the construction of equivariant barycenter maps, and applications to boundary dynamics, including C*-simplicity and Poisson boundaries. This provides a common perspective on recent geometric and dynamical results for groups acting on affine buildings.


Maria Cumplido Caballo

Title: Parabolic subgroups of Dyer groups

Abstract: Dyer groups form a class of groups containing Coxeter groups and right-angled Artin groups. We study parabolic subgroups of Dyer groups. In this work we address three main conjectures about these subgroups that remain open in Artin groups. We give an algorithm to decide whether two standard parabolic subgroups are conjugate and describe all conjugating elements in terms of ribbons. As a consequence, we obtain a description of the normaliser of a parabolic subgroup. We also prove the restandardisation property and deduce that arbitrary intersections of parabolic subgroups are parabolic, which implies the existence of parabolic closure for every element. This is joint work with Marina Salamero, Giovanni Sartori and Mireille Soergel.


Hendrik Van Maldeghem

Title: Involutions

Abstract: We investigate interesting fixed point structures of involutions acting on spherical buildings (mainly of exceptional type). We discover unexpected inclusions and highlight some combinatorial properties and connections.


Tom de Metz

Title: $AG_2$-graded Lie algebras

Abstract: Recently, Bernhard Mühlherr and Richard Weiss have discovered a class of Tits hexagons related to the (generalized) root system $AG_2$. They found two different families of examples: one class related to skew-hermitian forms and another class related to the exceptional groups $F_4$, $E_6$, $E_7$, and $E_8$, but the precise underlying algebraic structure remains mysterious. We approach this problem from a different angle, starting from Lie algebras graded by the root system $AG_2$, in the sense of Berman and Moody. It turns out—assuming char(k) is not 2 or 3—that such a Lie algebra is parametrized by a structurable algebra equipped with a “conjugate-supplementary idempotent”, i.e., an idempotent $t$ such that $t + \overline{t} = 1$. We can completely classify these examples, and in particular, we find that in the “most interesting” case, we recover the two classes found by Mühlherr and Weiss.


Bernhard Mühlherr

Title: Tits hexagons and hexagonic spaces

Abstract: RTits polygons are natural generalizations of Moufang polygons. Examples of Tits polygons can be obtained from spherical Moufang buildings using Tits indices. There are two families of Tits hexagons arising in this fashion. They are called of type $G_2$ and of type $AG_2$. In my talk I will recall the basics on Tits polygons with a special focus on the hexagon case. The aim is to explain two recent results: The first one (joint with Richard Weiss) is a partial classification of Tits hexagons of $type AG_2$.The second one (joint with Hendrik Van Maldeghem) is a point-line characterization of thick spherical buildings that is closely related to the combinatorics of the Tits hexagons of type $G_2$.


Stefan Witzel

Title: Two-dimensional Euclidean buildings are intricate

Abstract:Two-dimensional Euclidean buildings can be roughly classified by basic combinatorial data: type and thickness(es). However, each class contains many buildings that differ in more subtle ways. I will speak about properties that only depend on the basic combiatorial data and ones that distinguish between the more subtle properties. I will especially be interested in embeddings of finite subcomplexes and how they allow to construct various measures on the boundary. This is based on joint work with Jean Lécureux.