Mikolay Fraczyk: Benjamini-Schramm convergence for arithmetic hyperbolic 3-manifolds.

Speaker: Mikolay Fraczyk

Title: Benjamini-Schramm convergence for arithmetic hyperbolic 3-manifolds.

Abstract: I will talk about my recent result on the Benjamini-Schramm convergence of arithmetic hyperbolic 3-manifolds. Let $M$ be a hyperbolic arithmetic congruence manifold, i.e. a quotient $H^3/\Gamma$ where $\Gamma$ is a torsion free, arithmetic congruence lattice. Then the volume of the R-thin part is bounded by Vol(M_<R)\leq C_R \Vol(M)^{1-\alpha} where \alpha is a positive absolute constant and C_R>0 depends only on R. I will explain the idea of the proof, with  particular attention to the role played by the representation zeta functions and the character bounds for p-adic analytic groups.