Families of Discrete Representations from Incidence Theorems

par Jean-Philippe Burelle (Université de Sherbrooke)

lundi 5 oct. 2026, 16:00 → 17:15 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Motivated by a family of examples constructed by R. Schwartz based on Pappus's theorem, we explore constructions of representations of discrete groups arising from incidence theorems in projective spaces. Schwartz recently proved that his construction parametrizes the boundary of a connected component of Anosov representations in a certain moduli space of representations of PSL(2,Z) into Isom(SL(3,R)/SO(3)). We use a generalized version of Pappus's theorem to define a higher dimensional analogue of this family, and we prove that in RP³ these representations are "extended geometrically finite", a notion of relative Anosov representation introduced by T. Weisman. This is joint work in progress with W. Dimoune.