Buildings, surfaces and quaternions

Géométrie Dynamique

Lieu: 
Salle Duhem M3
Orateur: 
Alina Vdovina
Affiliation: 
University of Newcastle
Dates: 
Vendredi, 21 Septembre, 2018 - 10:15 - 11:15
Résumé: 

Buildings are exciting objects which have geometric, algebraic and number theoretical aspects. We will give elementary constructions of several classes of buildings as universal covers of finite complexes. Then, as a geometric application, we will show a connection of our results with Gromov's surface subgroup question, which asks whether each one-ended hyperbolic group contains a fundamental group of an orientable surface as a proper subgroup. As an arithmetic application we will give explicit examples of higher-dimensional quaternionic lattices, which are higher dimensional  analogues of earlier examples of Burger-Mozes, Rattaggi and Lubotzky-Phillips-Sarnak.