Seminar| Institute of Mathematical Sciences
Time: Thursday, November 6th, 2025,13:30-14:30
Location: RS408, IMS
Speaker: Junming Zhang, Nankai University
Abstract: The concept of Anosov representations, introduced by F. Labourie, plays an important role in the study of higher Teichmüller theory. Given a Riemann surface X, by the celebrated non-Abelian Hodge correspondence, reductive representations from the fundamental group of X into a Lie group correspond to polystable Higgs bundles. In general, it is hard to check the Anosov property of a representation corresponding to a given Higgs bundle other than the known higher Teichmuller spaces or some trivial embeddings of known Anosov representations. Recently, S. Filip proved that some weight 3 variations of Hodge structure define Anosov representations. We extend his result and discover the Anosov property of representations corresponding to more general families of $\mathrm{SO}_0(2,n+2)$-Higgs bundles.