On the dimension of limit sets on the real projective plane via stationary measures
Prof. Jialun Li
2023-11-21 14:30-16:00
MCM110&Zoom
Speaker: Prof. Jialun Li (École Polytechnique)Time: 14:30-16:00 Nov. 14 (Tuesday), Nov. 16 (Thursday), Nov. 21 (Tuesday)
Place: MCM110 & Online (Zoom ID: 3329836068 Password: mcm1234)
Title: On the dimension of limit sets on the real projective plane via stationary measures
Abstract: I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the affinity exponent. In particular, it exhibits a dimension jump under perturbation. The key tool is to study the stationary measures of finitely supported random walks on SL(3,R). We show the Hausdorff dimensions equal the Lyapunov dimensions under certain assumption. This is based on ongoing joint work with Wenyu Pan and Disheng Xu.
In the minicourse, I will also explain the two main ingredients of the proof: the entropy growth argument due to Hochman and the variational principle of the affinity exponent.
