Arithmeticity of strong approximate lattices
I will discuss a proof of the arithmeticity of strong approximate lattices in semi-simple Lie groups. The main technical novelty in the proof is a comparison theorem between the range of group homomorphisms of approximate lattices and the range of certain cocycles. I will then outline how to deduce superrigidity and arithmeticity results from this tool.
If time permits, I will also discuss recent developments around Arithmeticity results in more general settings.