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Homogeneous Dynamics and Anosov Representations: Higher rigidity properties of locally symmetric spaces

Presenter
April 24, 2026
SLMath
Keywords:
  • discrete subgroups
  • semisimple Lie groups
  • Anosov representations
  • convex projective geometry
  • entropy
  • geometric structures
  • Hitchin representations
  • homogeneous dynamics
  • mixing
  • thermodynamic formalism
  • thin subgroups
MSC:
  • 20-XX - Group theory and generalizations
  • 22-XX - Topological groups
  • Lie groups
  • 37-XX - Dynamical systems and ergodic theory
  • 53-XX - Differential geometry
  • 57-XX - Manifolds and cell complexes
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Abstract
We know that certain types of locally symmetric spaces are (very) rigid. What about Riemannian manifolds that look locally symmetric 99% of the time? Rigidity phenomena for these types of spaces are related to higher property (T), representation stability and the existence of a non-sofic group. Not much is known, but I will describe one result in this direction: a rigidity theorem for branched covers of octonionic hyperbolic manifolds with small branching locus. Based on a joint work with Ben Lowe.