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Benjamini-Schramm convergence of arithmetic orbifolds.

Presented by: 
Mikolaj Fraczyk
Wednesday 19th April 2017 - 10:00 to 11:00
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).

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