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Benjamini-Schramm convergence of arithmetic orbifolds.

Presented by: 
Mikolaj Fraczyk Université Paris-Sud 11
Tuesday 18th April 2017 -
11:30 to 12:30
INI Seminar Room 2
Let X be the a symmetric space. We say that a sequence of locally symmetric spaces Benjamini-Schramm converges to X if for any real number R the fraction of the volume taken by the R-thin part tends to 0. In my thesis I showed that for a cocompact, congruence arithmetic hyperbolic 3-manifold the volume of the R-thin part is less than a power less than one of the total volume. As a consequence, any sequence of such manifolds Benjamini-Schramm converges to hyperbolic 3-space. I will give some topological applications of this result. Lastly, I will discuss Benjamini-Schramm convergence of congruence arithmetic orbifolds covered by the symmetric spaces of real rank 1.   (joint work with Jean Raimbault).

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons