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Award ID contains: 2055122

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  1. ; (, Israel Journal of Mathematics)
    Abstract We prove a quantitative equidistribution statement for certain adelic homogeneous subsets in positive characteristic. As an application, we describe a proof of property (τ) for arithmetic groups in this context. 
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    Free, publicly-accessible full text available February 1, 2026
  2. ; (, Geometriae Dedicata)
    Abstract We prove a criterion for Benjamini-Schramm convergence of periodic orbits of Lie groups. This general observation is then applied to homogeneous spaces and the space of translation surfaces. 
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  3. ; ; (, Journal d'Analyse Mathématique)
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  4. ; (, Compositio Mathematica)
    We present a quantitative isolation property of the lifts of properly immersed geodesic planes in the frame bundle of a geometrically finite hyperbolic $$3$$ -manifold. Our estimates are polynomials in the tight areas and Bowen–Margulis–Sullivan densities of geodesic planes, with degree given by the modified critical exponents. 
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  5. ; (, Inventiones mathematicae)
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