Higher Teichmüller theory, and not-so-simple closed curves

par Charles Reid (MPI Leipzig)

vendredi 16 mai 2025, 14:00 → 15:00 Europe/Paris

112 (Bat. Braconnier)

A hyperbolic structure on a surface is captured by a representation of the fundamental group into PSL(2,R). Higher rank Teichmüller theory aims to go beyond hyperbolic geometry by studying representations into bigger lie groups, for instance PSL(n,R). I will discuss a "higher" version of one piece of hyperbolic geometry--Thurston's compactification of Teichmüller space. Boundary points of this compactification are measured laminations, certain objects generalizing simple closed curves. I will discuss compactifications of certain higher Teichmüller spaces where we will see closed curves with more intricate restrictions on self-intersection appearing in the boundary.